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Sommarmatte 1

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Nuvarande version (17 juli 2007 kl. 11.00) (redigera) (ogör)
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Rad 1: Rad 1:
__NOTOC__ __NOTOC__
-==Svar 1.1:1==+'''Svar 1.1:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$-7$</td> <td class="ntext" width="50%">$-7$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$1$</td> <td class="ntext" width="50%">$1$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$11$</td> <td class="ntext" width="50%">$11$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$1$</td> <td class="ntext" width="50%">$1$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.1:2==+'''Svar 1.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$0$</td> <td class="ntext" width="50%">$0$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$-1$</td> <td class="ntext" width="50%">$-1$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$-25$</td> <td class="ntext" width="50%">$-25$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$-19$</td> <td class="ntext" width="50%">$-19$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.1:3==+'''Svar 1.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
-<tr><td height="5px"/></tr>+
<tr align="left" valign="top"> <tr align="left" valign="top">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">heltalen, rationella talen</td> <td class="ntext" width="33%">heltalen, rationella talen</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
</tr> </tr>
<tr align="left" valign="top"> <tr align="left" valign="top">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">heltalen, rationella talen</td> <td class="ntext" width="33%">heltalen, rationella talen</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">heltalen, rationella talen</td> <td class="ntext" width="33%">heltalen, rationella talen</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
</tr> </tr>
<tr align="left" valign="top"> <tr align="left" valign="top">
-<td class="ntext">g)</td>+<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">rationella talen</td> <td class="ntext" width="33%">rationella talen</td>
-<td class="ntext">h)</td>+<td class="ntext">h)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
-<td class="ntext">i)</td>+<td class="ntext">i)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">irrationella talen</td> <td class="ntext" width="33%">irrationella talen</td>
</tr> </tr>
<tr align="left" valign="top"> <tr align="left" valign="top">
-<td class="ntext">j)</td>+<td class="ntext">j)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td>
-<td class="ntext">k)</td>+<td class="ntext">k)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">irrationella talen</td> <td class="ntext" width="33%">irrationella talen</td>
<td class="ntext">l)</td> <td class="ntext">l)</td>
<td class="ntext" width="33%">irrationella talen</td> <td class="ntext" width="33%">irrationella talen</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.1:4==+'''Svar 1.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$</td> <td class="ntext" width="100%">$\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$</td>
</tr> </tr>
<tr> <tr>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$</td> <td class="ntext" width="100%">$\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$</td>
</tr> </tr>
<tr> <tr>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$</td> <td class="ntext" width="100%">$\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.1:5==+'''Svar 1.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$1{,}167$</td> <td class="ntext" width="25%">$1{,}167$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$2{,}250$</td> <td class="ntext" width="25%">$2{,}250$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$0{,}286$</td> <td class="ntext" width="25%">$0{,}286$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$1{,}414$</td> <td class="ntext" width="25%">$1{,}414$</td>
</tr> </tr>
-<tr><td height="5px"/></tr>+ 
</table> </table>
</div> </div>
-==Svar 1.1:6==+'''Svar 1.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">Talet är rationellt och lika med $\,314/100 = 157/50\,$.</td> <td class="ntext" width="100%">Talet är rationellt och lika med $\,314/100 = 157/50\,$.</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.</td> <td class="ntext" width="100%">Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">Talet är rationellt och lika med $\,1999/9990\,$.</td> <td class="ntext" width="100%">Talet är rationellt och lika med $\,1999/9990\,$.</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">Talet är irrationellt.</td> <td class="ntext" width="100%">Talet är irrationellt.</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.2:1==+'''Svar 1.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{93}{28}$</td> <td class="ntext" width="33%">$\displaystyle \frac{93}{28}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{3}{35}$</td> <td class="ntext" width="33%">$\displaystyle \frac{3}{35}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle -\frac{7}{30}$</td> <td class="ntext" width="33%">$\displaystyle -\frac{7}{30}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{47}{60}$</td> <td class="ntext" width="33%">$\displaystyle \frac{47}{60}$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{47}{84}$</td> <td class="ntext" width="33%">$\displaystyle \frac{47}{84}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.2:2==+'''Svar 1.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle {30}$</td> <td class="ntext" width="50%">$\displaystyle {30}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle {8}$</td> <td class="ntext" width="50%">$\displaystyle {8}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle {84}$</td> <td class="ntext" width="50%">$\displaystyle {84}$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle {225}$</td> <td class="ntext" width="50%">$\displaystyle {225}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.2:3==+'''Svar 1.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
-<tr><td height="5px"/></tr>+ 
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle \frac{19}{100}$</td> <td class="ntext" width="50%">$\displaystyle \frac{19}{100}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle \frac{1}{240}$</td> <td class="ntext" width="50%">$\displaystyle \frac{1}{240}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.2:4==+'''Svar 1.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{6}{7}$</td> <td class="ntext" width="33%">$\displaystyle \frac{6}{7}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{16}{21}$</td> <td class="ntext" width="33%">$\displaystyle \frac{16}{21}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{1}{6}$</td> <td class="ntext" width="33%">$\displaystyle \frac{1}{6}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 1.2:5==+'''Svar 1.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
-<tr><td height="5px"/></tr>+ 
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{105}{4}$</td> <td class="ntext" width="33%">$\displaystyle \frac{105}{4}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$-5$</td> <td class="ntext" width="33%">$-5$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{8}{55}$</td> <td class="ntext" width="33%">$\displaystyle \frac{8}{55}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 1.2:6==+'''Svar 1.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table align="center" width="100%"><tr><td class="ntext" align="center">$\displaystyle \frac{152}{35}$</td></tr></table> +<table width="100%"><tr><td class="ntext">$\displaystyle \frac{152}{35}$</td></tr></table>
</div> </div>
-==&Ouml;vning 1.3:1==+'''Svar 1.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$72$</td> <td class="ntext" width="25%">$72$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$3$</td> <td class="ntext" width="25%">$3$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$-125$</td> <td class="ntext" width="25%">$-125$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$\displaystyle \frac{27}{8}$</td> <td class="ntext" width="25%">$\displaystyle \frac{27}{8}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 1.3:2==+'''Svar 1.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$2^6$</td> <td class="ntext" width="33%">$2^6$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$2^{-2}$</td> <td class="ntext" width="33%">$2^{-2}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$2^0$</td> <td class="ntext" width="33%">$2^0$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 1.3:3==+'''Svar 1.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="20%">$3^{-1}$</td> <td class="ntext" width="20%">$3^{-1}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="20%">$3^5$</td> <td class="ntext" width="20%">$3^5$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="20%">$3^4$</td> <td class="ntext" width="20%">$3^4$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="20%">$3^{-3}$</td> <td class="ntext" width="20%">$3^{-3}$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="20%">$3^{-3}$</td> <td class="ntext" width="20%">$3^{-3}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 1.3:4==+'''Svar 1.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$4$</td> <td class="ntext" width="33%">$4$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$3$</td> <td class="ntext" width="33%">$3$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$625$</td> <td class="ntext" width="33%">$625$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$16$</td> <td class="ntext" width="33%">$16$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{1}{3750}$</td> <td class="ntext" width="33%">$\displaystyle \frac{1}{3750}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 1.3:5==+'''Svar 1.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$2$</td> <td class="ntext" width="33%">$2$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{1}{2}$</td> <td class="ntext" width="33%">$\displaystyle \frac{1}{2}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$27$</td> <td class="ntext" width="33%">$27$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$2209$</td> <td class="ntext" width="33%">$2209$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$9$</td> <td class="ntext" width="33%">$9$</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{25}{3}$</td> <td class="ntext" width="33%">$\displaystyle \frac{25}{3}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
- +'''Svar 1.3:6'''
-==&Ouml;vning 1.3:6==+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<div class="ovning">+<table width="100%">
-<table width="100%" cellspacing="10px">+
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$256^{1/3}>200^{1/3}$</td> <td class="ntext" width="33%">$256^{1/3}>200^{1/3}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$0{,}4^{-3}>0{,}5^{-3}$</td> <td class="ntext" width="33%">$0{,}4^{-3}>0{,}5^{-3}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$0{,}2^{5}>0{,}2^{7}$</td> <td class="ntext" width="33%">$0{,}2^{5}>0{,}2^{7}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$</td> <td class="ntext" width="33%">$\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$125^{1/2}>625^{1/3}$</td> <td class="ntext" width="33%">$125^{1/2}>625^{1/3}$</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$3^{40}>2^{56}$</td> <td class="ntext" width="33%">$3^{40}>2^{56}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 2.1:1==+ 
-<div class="ovning">+'''Svar 2.1:1'''
-<table width="100%" cellspacing="10px">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$3x^2-3x$</td> <td class="ntext" width="33%">$3x^2-3x$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$xy+x^2y-x^3y$</td> <td class="ntext" width="33%">$xy+x^2y-x^3y$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$-4x^2+x^2y^2$</td> <td class="ntext" width="33%">$-4x^2+x^2y^2$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$x^3y-x^2y+x^3y^2$</td> <td class="ntext" width="33%">$x^3y-x^2y+x^3y^2$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$x^2-14x+49$</td> <td class="ntext" width="33%">$x^2-14x+49$</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$16y^2+40y+25$</td> <td class="ntext" width="33%">$16y^2+40y+25$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">g)</td>+<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$9x^6-6x^3y^2+y^4$</td> <td class="ntext" width="33%">$9x^6-6x^3y^2+y^4$</td>
-<td class="ntext">h)</td>+<td class="ntext">h)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$9x^{10}+30x^8+25x^6$</td> <td class="ntext" width="33%">$9x^{10}+30x^8+25x^6$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 2.1:2==+'''Svar 2.1:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$-5x^2+20$</td> <td class="ntext" width="50%">$-5x^2+20$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$10x-11$</td> <td class="ntext" width="50%">$10x-11$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$54x$</td> <td class="ntext" width="50%">$54x$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$81x^8-16$</td> <td class="ntext" width="50%">$81x^8-16$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$2a^2+2b^2$</td> <td class="ntext" width="50%">$2a^2+2b^2$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 2.1:3==+'''Svar 2.1:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$(x+6)(x-6)$</td> <td class="ntext" width="33%">$(x+6)(x-6)$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$5(x+2)(x-2)$</td> <td class="ntext" width="33%">$5(x+2)(x-2)$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$(x+3)^2$</td> <td class="ntext" width="33%">$(x+3)^2$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$(x-5)^2$</td> <td class="ntext" width="33%">$(x-5)^2$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$-2x(x+3)(x-3)$</td> <td class="ntext" width="33%">$-2x(x+3)(x-3)$</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$(4x+1)^2$</td> <td class="ntext" width="33%">$(4x+1)^2$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 2.1:4==+'''Svar 2.1:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$5\,$ framf&ouml;r $\,x^2\,$, $\,3\,$ framf&ouml;r $\,x$</td> <td class="ntext" width="100%">$5\,$ framf&ouml;r $\,x^2\,$, $\,3\,$ framf&ouml;r $\,x$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$2\,$ framf&ouml;r $\,x^2\,$, $\,1\,$ framf&ouml;r $\,x$</td> <td class="ntext" width="100%">$2\,$ framf&ouml;r $\,x^2\,$, $\,1\,$ framf&ouml;r $\,x$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">$\textrm{c)&nbsp;&nbsp;&nbsp; }$</td>
<td class="ntext" width="100%">$6\,$ framf&ouml;r $\,x^2\,$, $\,2\,$ framf&ouml;r $\,x$</td> <td class="ntext" width="100%">$6\,$ framf&ouml;r $\,x^2\,$, $\,2\,$ framf&ouml;r $\,x$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 2.1:5==+'''Svar 2.1:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle \frac{1}{1-x}$</td> <td class="ntext" width="50%">$\displaystyle \frac{1}{1-x}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$-\displaystyle \frac{1}{y(y+2)}$</td> <td class="ntext" width="50%">$-\displaystyle \frac{1}{y(y+2)}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$3(x-2)(x-1)$</td> <td class="ntext" width="50%">$3(x-2)(x-1)$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle \frac{2(y+2)}{y^2+4}$</td> <td class="ntext" width="50%">$\displaystyle \frac{2(y+2)}{y^2+4}$</td>
</tr> </tr>
Rad 457: Rad 436:
</div> </div>
-==Svar 2.1:6==+'''Svar 2.1:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$2y$</td> <td class="ntext" width="50%">$2y$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\displaystyle\frac{-x+12}{(x-2)(x+3)}$</td> <td class="ntext" width="50%">$\displaystyle\frac{-x+12}{(x-2)(x+3)}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
-<td class="ntext" width="50%">$\displaystyle\frac{b}{a(a-b)}$</td>+<td class="ntext" width="50%">$\displaystyle\frac{b}{a(a-b)&nbsp;&nbsp;&nbsp;}$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
-<td class="ntext" width="50%">$\displaystyle\frac{a(a+b)}{4b}$</td>+<td class="ntext" width="50%">$\displaystyle\frac{a(a+b)&nbsp;&nbsp;&nbsp;}{4b}$</td>
</tr> </tr>
</table> </table>
</div> </div>
-==Svar 2.1:7==+'''Svar 2.1:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{4}{(x+3)(x+5)}$</td> <td class="ntext" width="33%">$\displaystyle \frac{4}{(x+3)(x+5)}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{x^4-x^3+x^2+x-1}{x^2(x-1)}$</td> <td class="ntext" width="33%">$\displaystyle \frac{x^4-x^3+x^2+x-1}{x^2(x-1)}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{ax(a+1-x)}{(a+1)^2}$</td> <td class="ntext" width="33%">$\displaystyle \frac{ax(a+1-x)}{(a+1)^2}$</td>
</tr> </tr>
Rad 489: Rad 468:
</div> </div>
-==Svar 2.1:8==+'''Svar 2.1:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{x}{(x+3)(x+1)}$</td> <td class="ntext" width="33%">$\displaystyle \frac{x}{(x+3)(x+1)}$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{2(x-3)}{x}$</td> <td class="ntext" width="33%">$\displaystyle \frac{2(x-3)}{x}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{x+2}{2x+3}$</td> <td class="ntext" width="33%">$\displaystyle \frac{x+2}{2x+3}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 2.2:1==+'''Svar 2.2:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=1$</td> <td class="ntext" width="50%">$x=1$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=6$</td> <td class="ntext" width="50%">$x=6$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c) </td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp; </td>
<td class="ntext" width="50%">$x=-\displaystyle\frac{3}{2}$</td> <td class="ntext" width="50%">$x=-\displaystyle\frac{3}{2}$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=-\displaystyle\frac{13}{3}$</td> <td class="ntext" width="50%">$x=-\displaystyle\frac{13}{3}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 2.2:2==+'''Svar 2.2:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=1$</td> <td class="ntext" width="50%">$x=1$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=\displaystyle\frac{5}{3}$</td> <td class="ntext" width="50%">$x=\displaystyle\frac{5}{3}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=2$</td> <td class="ntext" width="50%">$x=2$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$x=-2$</td> <td class="ntext" width="50%">$x=-2$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==Svar 2.2:3==+'''Svar 2.2:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$x=9$</td> <td class="ntext" width="100%">$x=9$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$x=\displaystyle\frac{7}{5}$</td> <td class="ntext" width="100%">$x=\displaystyle\frac{7}{5}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c) </td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp; </td>
<td class="ntext" width="100%">$x=\displaystyle\frac{4}{5}$</td> <td class="ntext" width="100%">$x=\displaystyle\frac{4}{5}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d) </td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp; </td>
<td class="ntext" width="100%">$x=\displaystyle\frac{1}{2}$</td> <td class="ntext" width="100%">$x=\displaystyle\frac{1}{2}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.2:4==+'''Svar 2.2:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td>a)</td>+<td>a)&nbsp;&nbsp;&nbsp;</td>
<td width="100%">$-2x+y=3$</td> <td width="100%">$-2x+y=3$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td>b)</td>+<td>b)&nbsp;&nbsp;&nbsp;</td>
<td width="100%">$y=-\displaystyle\frac{3}{4}x+\frac{5}{4}$</td> <td width="100%">$y=-\displaystyle\frac{3}{4}x+\frac{5}{4}$</td>
</tr> </tr>
Rad 580: Rad 555:
</div> </div>
-==&Ouml;vning 2.2:5==+'''Svar 2.2:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$y=-3x+9$</td> <td class="ntext" width="100%">$y=-3x+9$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$y=-3x+1$</td> <td class="ntext" width="100%">$y=-3x+1$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$y=3x+5$</td> <td class="ntext" width="100%">$y=3x+5$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$y=-\displaystyle \frac{1}{2}x+5$</td> <td class="ntext" width="100%">$y=-\displaystyle \frac{1}{2}x+5$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$k = \displaystyle\frac{8}{5}$</td> <td class="ntext" width="100%">$k = \displaystyle\frac{8}{5}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.2:6==+'''Svar 2.2:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\bigl(-\frac{5}{3},0\bigr)$</td> <td class="ntext" width="50%">$\bigl(-\frac{5}{3},0\bigr)$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$(0,5)$</td> <td class="ntext" width="50%">$(0,5)$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\bigl(0,-\frac{6}{5}\bigr)$</td> <td class="ntext" width="50%">$\bigl(0,-\frac{6}{5}\bigr)$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$(12,-13)$</td> <td class="ntext" width="50%">$(12,-13)$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\bigl(-\frac{1}{4},\frac{3}{2}\bigr)$</td> <td class="ntext" width="50%">$\bigl(-\frac{1}{4},\frac{3}{2}\bigr)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.2:7==+'''Svar 2.2:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">[[Bild:Svar_o2_2_7a.gif‎]] </td> <td class="ntext" width="33%">[[Bild:Svar_o2_2_7a.gif‎]] </td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">[[Bild:Svar_o2_2_7b.gif‎]] </td> <td class="ntext" width="33%">[[Bild:Svar_o2_2_7b.gif‎]] </td>
</tr><tr> </tr><tr>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">[[Bild:Svar_o2_2_7c.gif‎]] </td> <td class="ntext" width="33%">[[Bild:Svar_o2_2_7c.gif‎]] </td>
</tr> </tr>
Rad 645: Rad 618:
</div> </div>
-==&Ouml;vning 2.2:8==+'''Svar 2.2:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
<table width="100%"> <table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">[[Bild:Svar_o2_2_8a.gif‎]]</td> <td class="ntext" width="33%">[[Bild:Svar_o2_2_8a.gif‎]]</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">[[Bild:Svar_o2_2_8b.gif‎]]</td> <td class="ntext" width="33%">[[Bild:Svar_o2_2_8b.gif‎]]</td>
</tr><tr> </tr><tr>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">[[Bild:Svar_o2_2_8c.gif‎]]</td> <td class="ntext" width="33%">[[Bild:Svar_o2_2_8c.gif‎]]</td>
</tr> </tr>
Rad 660: Rad 633:
</div> </div>
-==&Ouml;vning 2.2:9==+'''Svar 2.2:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$4\,$ a.e.</td> <td class="ntext" width="100%">$4\,$ a.e.</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$5\,$ a.e.</td> <td class="ntext" width="100%">$5\,$ a.e.</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$6\,$ a.e.</td> <td class="ntext" width="100%">$6\,$ a.e.</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:1==+'''Svar 2.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$(x-1)^2-1$</td> <td class="ntext" width="25%">$(x-1)^2-1$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$(x+1)^2-2$</td> <td class="ntext" width="25%">$(x+1)^2-2$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$-(x-1)^2+6$</td> <td class="ntext" width="25%">$-(x-1)^2+6$</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="25%">$\bigl(x+\frac{5}{2}\bigr)^2-\frac{13}{4}$</td> <td class="ntext" width="25%">$\bigl(x+\frac{5}{2}\bigr)^2-\frac{13}{4}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:2==+'''Svar 2.3:2'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
-<tr><td height="5px"/></tr>+
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\left\{ \eqalign{ x_1 &= 1 \cr x_2 &= 3\cr }\right.$</td> <td class="ntext" width="33%">$\left\{ \eqalign{ x_1 &= 1 \cr x_2 &= 3\cr }\right.$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\left\{ \eqalign{ y_1 &= -5 \cr y_2 &= 3\cr }\right.$</td> <td class="ntext" width="33%">$\left\{ \eqalign{ y_1 &= -5 \cr y_2 &= 3\cr }\right.$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
-<td class="ntext" width="33%"> saknar (reella) l&ouml;sning</td>+<td class="ntext" width="33%"> saknar (reella)&nbsp;&nbsp;&nbsp; l&ouml;sning</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$ \left\{ \eqalign{ x_1 &= \textstyle\frac{1}{2}\cr x_2 &= \textstyle\frac{13}{2}\cr }\right.$</td> <td class="ntext" width="33%">$ \left\{ \eqalign{ x_1 &= \textstyle\frac{1}{2}\cr x_2 &= \textstyle\frac{13}{2}\cr }\right.$</td>
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\left\{ \eqalign{ x_1 &= -1 \cr x_2 &= \textstyle\frac{3}{5}\cr }\right.$</td> <td class="ntext" width="33%">$\left\{ \eqalign{ x_1 &= -1 \cr x_2 &= \textstyle\frac{3}{5}\cr }\right.$</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$ \left\{ \eqalign{ x_1 &= \textstyle\frac{4}{3}\cr x_2 &= 2\cr }\right.$</td> <td class="ntext" width="33%">$ \left\{ \eqalign{ x_1 &= \textstyle\frac{4}{3}\cr x_2 &= 2\cr }\right.$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:3==+'''Svar 2.3:3'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\left\{ \eqalign{ x_1 &= 0 \cr x_2 & = -3\cr }\right.$</td> <td class="ntext" width="50%">$\left\{ \eqalign{ x_1 &= 0 \cr x_2 & = -3\cr }\right.$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\left\{ \eqalign{ x_1 &= 3 \cr x_2 & = -5\cr }\right. $</td> <td class="ntext" width="50%">$\left\{ \eqalign{ x_1 &= 3 \cr x_2 & = -5\cr }\right. $</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\left\{ \eqalign{ x_1 & = \textstyle\frac{2}{3} \cr x_2 & = -8\cr }\right. $</td> <td class="ntext" width="50%">$\left\{ \eqalign{ x_1 & = \textstyle\frac{2}{3} \cr x_2 & = -8\cr }\right. $</td>
-<td class="ntext">d)</td>+<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\left\{ \eqalign{ x_1 & = 0\cr x_2 & = 12\cr }\right. $</td> <td class="ntext" width="50%">$\left\{ \eqalign{ x_1 & = 0\cr x_2 & = 12\cr }\right. $</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">e)</td>+<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\left\{ \eqalign{ x_1 & = -3 \cr x_2 & = 8\cr }\right. $</td> <td class="ntext" width="50%">$\left\{ \eqalign{ x_1 & = -3 \cr x_2 & = 8\cr }\right. $</td>
-<td class="ntext">f)</td>+<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="50%">$\left\{ \eqalign{ x_1 & = 0 \cr x_2 & = 1 \cr x_3 & = 2 }\right. $</td> <td class="ntext" width="50%">$\left\{ \eqalign{ x_1 & = 0 \cr x_2 & = 1 \cr x_3 & = 2 }\right. $</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:4==+'''Svar 2.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$ax^2-ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.</td> <td class="ntext" width="100%">$ax^2-ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$ax^2-2ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.</td> <td class="ntext" width="100%">$ax^2-2ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$ax^2-(3+\sqrt{3}\,)ax+3\sqrt{3}\,a=0\,$, där $\,a\ne 0\,$ är en konstant.</td> <td class="ntext" width="100%">$ax^2-(3+\sqrt{3}\,)ax+3\sqrt{3}\,a=0\,$, där $\,a\ne 0\,$ är en konstant.</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:5==+'''Svar 2.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">Exempelvis $\ x^2+14x+49=0\,$.</td> <td class="ntext" width="100%">Exempelvis $\ x^2+14x+49=0\,$.</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$3< x<4$</td> <td class="ntext" width="100%">$3< x<4$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="100%">$b=-5$</td> <td class="ntext" width="100%">$b=-5$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:6==+'''Svar 2.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$0$</td> <td class="ntext" width="33%">$0$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$-2$</td> <td class="ntext" width="33%">$-2$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle \frac{3}{4}$</td> <td class="ntext" width="33%">$\displaystyle \frac{3}{4}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:7==+'''Svar 2.3:7'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$1$</td> <td class="ntext" width="33%">$1$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$\displaystyle -\frac{7}{4}$</td> <td class="ntext" width="33%">$\displaystyle -\frac{7}{4}$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">saknar max</td> <td class="ntext" width="33%">saknar max</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:8==+'''Svar 2.3:8'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
<td>Se lösningen i <td>Se lösningen i
Rad 824: Rad 788:
</div> </div>
-==&Ouml;vning 2.3:9==+'''Svar 2.3:9'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$(-1,0)\ $ och $\ (1,0)$</td> <td class="ntext" width="33%">$(-1,0)\ $ och $\ (1,0)$</td>
-<td class="ntext">b)</td>+<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$(2,0)\ $ och $\ (3,0)$</td> <td class="ntext" width="33%">$(2,0)\ $ och $\ (3,0)$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$(1,0)\ $ och $\ (3,0)$</td> <td class="ntext" width="33%">$(1,0)\ $ och $\ (3,0)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
</table> </table>
</div> </div>
-==&Ouml;vning 2.3:10==+'''Svar 2.3:10'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
<td>Se lösningen i webmaterialet när du loggat in till kursen</td> <td>Se lösningen i webmaterialet när du loggat in till kursen</td>
Rad 847: Rad 810:
</table> </table>
</div> </div>
 +'''Svar 3.1:1'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$2^{1/2}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$7^{5/2}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$3^{4/3}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$3^{1/4}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.1:2'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$3$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$3$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">ej definierad</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$5^{11/6}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$12$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$2$</td>
 +<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$-5$</td>
 +<td></td>
 +<td></td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.1:3'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$3$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle \frac{4\sqrt{3}}{3}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$2\sqrt{5}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$2-\sqrt{2}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.1:4'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$0{,}4$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$0{,}3$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$-4\sqrt{2}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$2\sqrt{3}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.1:5'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{\sqrt{3}}{3}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{7^{2/3}}{7}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$3-\sqrt{7}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.1:6'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$6+2\sqrt{2}+3\sqrt{5}+\sqrt{10}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$-\displaystyle \frac{5+4\sqrt{3}}{23}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle \frac{2}{3}\sqrt{6}+\displaystyle \frac{2}{3}\sqrt{3}-\displaystyle \frac{2}{5}\sqrt{10}-\displaystyle \frac{2}{5}\sqrt{5}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.1:7'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\sqrt{5}-\sqrt{7}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$-\sqrt{35}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\sqrt{17}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.1:8'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$7 > \sqrt7$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sqrt7 > 2{,}5$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.2:1'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$x=5$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.2:2'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$x=1$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.2:3'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$\left \{ \eqalign{ x_1 & = 3 \cr x_2 & = 4\cr } \right.$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.2:4'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">Saknar l&ouml;sning.</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.2:5'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$x=1$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.2:6'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$x=\displaystyle\frac{5}{4}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.3:1'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=3$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=-1$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=-2$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=4$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.3:2'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$-1$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$4$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$-3$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$0$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$2$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$3$</td>
 +<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$10$</td>
 +<td class="ntext">h)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$-2$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.3:3'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$3$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$-\displaystyle \frac{1}{2}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$-3$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{7}{3}$</td>
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$4$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$-2$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$1$</td>
 +<td class="ntext">h)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{5}{2}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.3:4'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$1$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$0$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$-\displaystyle \frac{1}{2}\lg{3}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.3:5'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$5$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$0$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$0$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$0$</td>
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$-2$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$e^2$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.3:6'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%" >
 +<tr align="left"><td height="5px"/></tr>
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$1{,}262$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$1{,}663$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$4{,}762$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.4:1'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$x=\ln 13$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$x=\displaystyle\frac{\ln 2 - \ln 13}{1+\ln 3}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$x=\displaystyle\frac{\ln 7 - \ln 3}{1-\ln 2}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.4:2'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$ \left\{ \eqalign{ x_1&=\sqrt2 \cr x_2&=-\sqrt2 } \right. $</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$x=\ln \left(\displaystyle\frac{\sqrt17}{2}-\frac{1}{2}\right)$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">Saknar l&ouml;sning</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 3.4:3'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=-\,\displaystyle\frac{1}{\ln{2}}\pm\sqrt{\left(\displaystyle\frac{1}{\ln{2}}\right)^2-1}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=\displaystyle \frac{5}{2}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=1$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:1'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$90^\circ\ $ och $\ \displaystyle \frac{\pi}{2} \textrm{ rad} $</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$135^\circ\ $ och $\ \displaystyle \frac{3\pi}{4} \textrm{ rad}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$-240^\circ\ $ och $\ \displaystyle -\frac{4\pi}{3} \textrm{ rad}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$2910^\circ\ $ och $\ \displaystyle \frac{97\pi}{6} \textrm{ rad}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:2'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{\pi}{4}\textrm{ rad}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{3\pi}{4}\textrm{ rad}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$-\displaystyle \frac{7\pi}{20}\textrm{ rad}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{3\pi}{2}\textrm{ rad}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:3'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$x=50$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$x=5$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$x=15$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:4'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$5 \textrm{ l.e.}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$\sqrt{61} \textrm{ l.e.}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$(2,0)$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:5'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$(x-1)^2+(y-2)^2=4$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$(x-2)^2+(y+1)^2=13$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:6'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">En cirkel med radie 3 och medelpunkt i origo.</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">En cirkel med radie $\sqrt 3$ och medelpunkt i punkten (1, 2).</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">En cirkel med radie $\frac{1}{3}\sqrt 10$ och medelpunkt i punkten (1/3, -7/3).</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:7'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">En cirkel med medelpunkt (-1, 1) och radie $\sqrt 3$.</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">En cirkel med medelpunkt (0, -2) och radie 2. </td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">En cirkel med medelpunkt (1, -3) och radie $\sqrt 7$.</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">Endast punkten (1, -1). </td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:8'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">
 +$\displaystyle \frac{10}{\pi}\textrm{ varv }\approx 3,2 \textrm{ varv} $ </td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.1:9'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$\displaystyle \frac{32\pi}{3} \textrm{ cm}^2 \approx 33,5 \textrm{ cm}^2$</td>
 +</tr>
 +</table>
 +
 +</div>
 +
 +'''Svar 4.1:10'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$x=9$ dm</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.2:1'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +Facit till alla delfrågor<br \>
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%"> $x=13\cdot\tan {27 ^\circ} \approx 6{,}62$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=25\cdot\cos {32 ^\circ} \approx 21{,}2$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=\displaystyle\frac{14}{\tan {40 ^\circ}} \approx 16{,}7$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=\displaystyle\frac{16}{\cos {20 ^\circ}} \approx 17{,}0$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=\displaystyle\frac{11}{\sin {35 ^\circ}} \approx 19{,}2$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=\displaystyle\frac{19}{\tan {50 ^\circ}} \approx 15{,}9$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.2:2'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%"> $\tan v=\displaystyle\frac{2}{5}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sin v=\displaystyle\frac{7}{11}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\cos v=\displaystyle\frac{5}{7}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sin v=\displaystyle\frac{3}{5}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$v=30 ^\circ$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sin \displaystyle\frac{v}{2}=\displaystyle\frac{1}{3}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.2:3'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$-1$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$1$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$0$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$0$</td>
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{1}{\sqrt{2}}$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{\sqrt{3}}{2}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.2:4'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{\sqrt{3}}{2}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{1}{2}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$-1$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$0$</td>
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{1}{\sqrt{3}}$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$\sqrt{3}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.2:5'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$-\displaystyle \frac{1}{\sqrt{2}}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$1$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$\displaystyle \frac{\sqrt{3}}{2}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="25%">$-1$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.2:6'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$x= \sqrt{3}-1$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.2:7'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">Älvens bredd är $\ \displaystyle\frac{100}{\sqrt{3}-1}$ m $\approx 136{,}6$ m.</td>
 +</tr>
 +</table>
 +</div>
 +
 +
 +'''Svar 4.2:8'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$\ell\cos \gamma=a \cos \alpha - b\cos \beta $</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.2:9'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">Avståndet är $\ \sqrt{205-48\sqrt{3}} \approx 11{,}0$ km.</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:1'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$v = \displaystyle \frac{9\pi}{5}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$v = \displaystyle \frac{6\pi}{7}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">$v = \displaystyle \frac{9\pi}{7}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:2'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$v=\displaystyle \frac{\pi}{2}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$v=\displaystyle \frac{3\pi}{5}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:3'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$-a$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$a$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sqrt{1-a^2}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sqrt{1-a^2}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$-a$</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle \frac{\sqrt{3}}{2}\sqrt{1-a^2}+\displaystyle \frac{1}{2}\cdot a $</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:4'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$1-b^2$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sqrt{1-b^2}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$2b\sqrt{1-b^2}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$2b^2-1$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sqrt{1-b^2}\cdot\displaystyle \frac{1}{\sqrt{2}} + b\cdot \displaystyle \frac{1}{\sqrt{2}} $</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$b\cdot\displaystyle \frac{1}{2}+\sqrt{1-b^2}\cdot\displaystyle \frac{\sqrt{3}}{2}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:5'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext" width="100%">$\cos{v}=\displaystyle \frac{2\sqrt{6}}{7}\quad$ och $\quad\tan{v}=\displaystyle \frac{5}{2\sqrt{6}}\,$.</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:6'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$\sin{v}=-\displaystyle \frac{\sqrt{7}}{4}\quad$ och $\quad\tan{v}=-\displaystyle \frac{\sqrt{7}}{3}\,$.</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$\cos{v}=-\displaystyle \frac{\sqrt{91}}{10}\quad$ och $\quad\tan{v}=-\displaystyle \frac{3}{\sqrt{91}}\,$.</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\sin{v}=-\displaystyle \frac{3}{\sqrt{10}}\quad$ och $\quad\cos{v}=-\displaystyle \frac{1}{\sqrt{10}}\,$.</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:7'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$\sin{(x+y)}=\displaystyle \frac{4\sqrt{2}+\sqrt{5}}{9}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="100%">$\sin{(x+y)}=\displaystyle \frac{3\sqrt{21}+8}{25}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:8'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">Se lösningen i webmaterialet när
 +du loggat in till kursen</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.3:9'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">Se lösningen i webmaterialet när
 +du loggat in till kursen</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.4:1'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{6}\,$, $\,\displaystyle v=\frac{5\pi}{6}$</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{3}\,$, $\,\displaystyle v=\frac{5\pi}{3}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{2}$</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle v=\frac{\pi}{4}\,$, $\,\displaystyle v=\frac{5\pi}{4}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">lösning saknas</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle v=\frac{11\pi}{6}\,$, $\,\displaystyle v=\frac{7\pi}{6}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">g)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$\displaystyle v=\frac{5\pi}{6}\,$, $\,\displaystyle v=\frac{11\pi}{6}$</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.4:2'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">
 +$\left\{\eqalign{
 +x&=\displaystyle\frac{\pi}{3}+2n\pi\cr
 +x&=\displaystyle\frac{2\pi}{3}+2n\pi } \right.$
 +</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">
 +$\left\{\eqalign{
 +x&=\displaystyle\frac{\pi}{3}+2n\pi\cr
 +x&=\displaystyle\frac{5\pi}{3}+2n\pi } \right.$
 +</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">
 +$x=n\pi$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">
 +$\left\{\eqalign{
 +x&=\displaystyle\frac{\pi}{20}+\displaystyle\frac{2n\pi}{5}\cr
 +x&=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.$
 +</td>
 +<td class="ntext">e)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">
 +$\left\{\eqalign{
 +x&=\displaystyle\frac{\pi}{30}+\displaystyle\frac{2n\pi}{5}\cr
 +x&=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2n\pi}{5}} \right.$
 +</td>
 +<td class="ntext">f)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="33%">
 +$\left\{\eqalign{
 +x&=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2n\pi}{3}\cr
 +x&=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2n\pi}{3}} \right.$
 +</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.4:3'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=\displaystyle\frac{\pi}{6}+2n\pi\cr
 +x&=\displaystyle\frac{11\pi}{6}+2n\pi
 +}\right.$
 +</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=\displaystyle\frac{\pi}{5}+2n\pi\cr
 +x&=\displaystyle\frac{4\pi}{5}+2n\pi
 +}\right.$
 +</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=25^\circ + n\cdot 360^\circ\cr
 +x&=75^\circ + n\cdot 360^\circ
 +}\right.$
 +</td>
 +<td class="ntext">d)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=5^\circ + n \cdot 120^\circ \cr
 +x&= 55^\circ + n \cdot 120^\circ
 +}\right.$
 +</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.4:4'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%" cellpadding="10px">
 +<tr>
 +<td align="left">
 +$v_1=50^\circ$, $\ \ v_2=120^\circ$, $\ \ v_3=230^\circ\ \ $ och $\ \ v_4=300^\circ$
 +</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.4:5'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=n\pi\cr
 +x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2}
 +}\right.$
 +</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=\displaystyle \frac{n\pi}{3}$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=\displaystyle \frac{\pi}{20}+\displaystyle \frac{n\pi}{2}\cr
 +x&=-\displaystyle \frac{\pi}{30}+\displaystyle \frac{n\pi}{3}
 +}\right.$
 +</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.4:6'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$x=n\pi$
 +</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=\displaystyle \frac{\pi}{4}+2n\pi\cr
 +x&=\displaystyle \frac{\pi}{2}+n\pi\cr
 +x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$
 +</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=\displaystyle \frac{2n\pi}{3}\cr
 +x&=\displaystyle \pi + 2n\pi\cr
 +}\right.$
 +</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.4:7'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{ \matrix{
 +x=\displaystyle \frac{\pi}{6}+2n\pi\cr
 +x=\displaystyle \frac{5\pi}{6}+2n\pi\cr
 +x=\displaystyle \frac{3\pi}{2}+2n\pi
 +}\right.$
 +</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=\pm \displaystyle \frac{\pi}{3} + 2n\pi $</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{ \matrix{
 +x=\displaystyle \frac{\pi}{2}+2n\pi\cr
 +x=\displaystyle \frac{\pi}{14}+\displaystyle \frac{2n\pi}{7}
 +}\right.$
 +</td>
 +</tr>
 +</table>
 +</div>
 +
 +'''Svar 4.4:8'''
 +<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
 +<table width="100%">
 +<tr align="left">
 +<td class="ntext">a)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=\displaystyle \frac{\pi}{4}+2n\pi\cr
 +x&=\displaystyle \frac{\pi}{2}+n\pi\cr
 +x&=\displaystyle \frac{3\pi}{4}+2n\pi
 +}\right.$
 +</td>
 +<td class="ntext">b)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">$x=\displaystyle \frac{\pi}{3}+n\pi$</td>
 +<td class="ntext">c)&nbsp;&nbsp;&nbsp;</td>
 +<td class="ntext" width="50%">
 +$\left\{\eqalign{
 +x&=n\pi\cr
 +x&=\displaystyle \frac{3\pi}{4}+n\pi
 +}\right.$
 +</td>
 +</tr>
 +</table>
 +</div>
 +
 +<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>
 +<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br><br>
 +<br><br><br><br><br><br><br><br><br>

Nuvarande version

Svar 1.1:1

a)    $-7$ b)    $1$
c)    $11$ d)    $1$

Svar 1.1:2

a)    $0$ b)    $-1$
c)    $-25$ d)    $-19$

Svar 1.1:3

a)    naturliga talen, heltalen, rationella talen b)    heltalen, rationella talen c)    naturliga talen, heltalen, rationella talen
d)    heltalen, rationella talen e)    heltalen, rationella talen f)    naturliga talen, heltalen, rationella talen
g)    rationella talen h)    naturliga talen, heltalen, rationella talen i)    irrationella talen
j)    naturliga talen, heltalen, rationella talen k)    irrationella talen l) irrationella talen

Svar 1.1:4

a)    $\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$
b)    $\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$
c)    $\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$

Svar 1.1:5

a)    $1{,}167$ b)    $2{,}250$ c)    $0{,}286$ d)    $1{,}414$

Svar 1.1:6

a)    Talet är rationellt och lika med $\,314/100 = 157/50\,$.
b)    Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.
c)    Talet är rationellt och lika med $\,1999/9990\,$.
d)    Talet är irrationellt.

Svar 1.2:1

a)    $\displaystyle \frac{93}{28}$ b)    $\displaystyle \frac{3}{35}$ c)    $\displaystyle -\frac{7}{30}$
d)    $\displaystyle \frac{47}{60}$ e)    $\displaystyle \frac{47}{84}$

Svar 1.2:2

a)    $\displaystyle {30}$ b)    $\displaystyle {8}$
c)    $\displaystyle {84}$ d)    $\displaystyle {225}$

Svar 1.2:3

a)    $\displaystyle \frac{19}{100}$ b)    $\displaystyle \frac{1}{240}$

Svar 1.2:4

a)    $\displaystyle \frac{6}{7}$ b)    $\displaystyle \frac{16}{21}$ c)    $\displaystyle \frac{1}{6}$

Svar 1.2:5

a)    $\displaystyle \frac{105}{4}$ b)    $-5$ c)    $\displaystyle \frac{8}{55}$

Svar 1.2:6

$\displaystyle \frac{152}{35}$

Svar 1.3:1

a)    $72$ b)    $3$ c)    $-125$ d)    $\displaystyle \frac{27}{8}$

Svar 1.3:2

a)    $2^6$ b)    $2^{-2}$ c)    $2^0$

Svar 1.3:3

a)    $3^{-1}$ b)    $3^5$ c)    $3^4$ d)    $3^{-3}$ e)    $3^{-3}$

Svar 1.3:4

a)    $4$ b)    $3$ c)    $625$
d)    $16$ e)    $\displaystyle \frac{1}{3750}$

Svar 1.3:5

a)    $2$ b)    $\displaystyle \frac{1}{2}$ c)    $27$
d)    $2209$ e)    $9$ f)    $\displaystyle \frac{25}{3}$

Svar 1.3:6

a)    $256^{1/3}>200^{1/3}$ b)    $0{,}4^{-3}>0{,}5^{-3}$ c)    $0{,}2^{5}>0{,}2^{7}$
d)    $\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$ e)    $125^{1/2}>625^{1/3}$ f)    $3^{40}>2^{56}$

Svar 2.1:1

a)    $3x^2-3x$ b)    $xy+x^2y-x^3y$ c)    $-4x^2+x^2y^2$
d)    $x^3y-x^2y+x^3y^2$ e)    $x^2-14x+49$ f)    $16y^2+40y+25$
g)    $9x^6-6x^3y^2+y^4$ h)    $9x^{10}+30x^8+25x^6$

Svar 2.1:2

a)    $-5x^2+20$ b)    $10x-11$
c)    $54x$ d)    $81x^8-16$
e)    $2a^2+2b^2$

Svar 2.1:3

a)    $(x+6)(x-6)$ b)    $5(x+2)(x-2)$ c)    $(x+3)^2$
d)    $(x-5)^2$ e)    $-2x(x+3)(x-3)$ f)    $(4x+1)^2$

Svar 2.1:4

a)    $5\,$ framför $\,x^2\,$, $\,3\,$ framför $\,x$
b)    $2\,$ framför $\,x^2\,$, $\,1\,$ framför $\,x$
$\textrm{c)    }$ $6\,$ framför $\,x^2\,$, $\,2\,$ framför $\,x$

Svar 2.1:5

a)    $\displaystyle \frac{1}{1-x}$ b)    $-\displaystyle \frac{1}{y(y+2)}$
c)    $3(x-2)(x-1)$ d)    $\displaystyle \frac{2(y+2)}{y^2+4}$

Svar 2.1:6

a)    $2y$ b)    $\displaystyle\frac{-x+12}{(x-2)(x+3)}$
c)    $\displaystyle\frac{b}{a(a-b)   }$ d)    $\displaystyle\frac{a(a+b)   }{4b}$

Svar 2.1:7

a)    $\displaystyle \frac{4}{(x+3)(x+5)}$ b)    $\displaystyle \frac{x^4-x^3+x^2+x-1}{x^2(x-1)}$ c)    $\displaystyle \frac{ax(a+1-x)}{(a+1)^2}$

Svar 2.1:8

a)    $\displaystyle \frac{x}{(x+3)(x+1)}$ b)    $\displaystyle \frac{2(x-3)}{x}$ c)    $\displaystyle \frac{x+2}{2x+3}$

Svar 2.2:1

a)    $x=1$ b)    $x=6$
c)    $x=-\displaystyle\frac{3}{2}$ d)    $x=-\displaystyle\frac{13}{3}$

Svar 2.2:2

a)    $x=1$ b)    $x=\displaystyle\frac{5}{3}$
c)    $x=2$ d)    $x=-2$

Svar 2.2:3

a)    $x=9$
b)    $x=\displaystyle\frac{7}{5}$
c)    $x=\displaystyle\frac{4}{5}$
d)    $x=\displaystyle\frac{1}{2}$

Svar 2.2:4

a)    $-2x+y=3$
b)    $y=-\displaystyle\frac{3}{4}x+\frac{5}{4}$

Svar 2.2:5

a)    $y=-3x+9$
b)    $y=-3x+1$
c)    $y=3x+5$
d)    $y=-\displaystyle \frac{1}{2}x+5$
e)    $k = \displaystyle\frac{8}{5}$

Svar 2.2:6

a)    $\bigl(-\frac{5}{3},0\bigr)$ b)    $(0,5)$
c)    $\bigl(0,-\frac{6}{5}\bigr)$ d)    $(12,-13)$
e)    $\bigl(-\frac{1}{4},\frac{3}{2}\bigr)$

Svar 2.2:7

a)    Bild:Svar_o2_2_7a.gif‎ b)    Bild:Svar_o2_2_7b.gif‎
c)    Bild:Svar_o2_2_7c.gif‎

Svar 2.2:8

a)    Bild:Svar_o2_2_8a.gif‎ b)    Bild:Svar_o2_2_8b.gif‎
c)    Bild:Svar_o2_2_8c.gif‎

Svar 2.2:9

a)    $4\,$ a.e.
b)    $5\,$ a.e.
c)    $6\,$ a.e.


Svar 2.3:1

a)    $(x-1)^2-1$ b)    $(x+1)^2-2$ c)    $-(x-1)^2+6$ d)    $\bigl(x+\frac{5}{2}\bigr)^2-\frac{13}{4}$

Svar 2.3:2

a)    $\left\{ \eqalign{ x_1 &= 1 \cr x_2 &= 3\cr }\right.$ b)    $\left\{ \eqalign{ y_1 &= -5 \cr y_2 &= 3\cr }\right.$ c)    saknar (reella)    lösning
d)    $ \left\{ \eqalign{ x_1 &= \textstyle\frac{1}{2}\cr x_2 &= \textstyle\frac{13}{2}\cr }\right.$ e)    $\left\{ \eqalign{ x_1 &= -1 \cr x_2 &= \textstyle\frac{3}{5}\cr }\right.$ f)    $ \left\{ \eqalign{ x_1 &= \textstyle\frac{4}{3}\cr x_2 &= 2\cr }\right.$

Svar 2.3:3

a)    $\left\{ \eqalign{ x_1 &= 0 \cr x_2 & = -3\cr }\right.$ b)    $\left\{ \eqalign{ x_1 &= 3 \cr x_2 & = -5\cr }\right. $
c)    $\left\{ \eqalign{ x_1 & = \textstyle\frac{2}{3} \cr x_2 & = -8\cr }\right. $ d)    $\left\{ \eqalign{ x_1 & = 0\cr x_2 & = 12\cr }\right. $
e)    $\left\{ \eqalign{ x_1 & = -3 \cr x_2 & = 8\cr }\right. $ f)    $\left\{ \eqalign{ x_1 & = 0 \cr x_2 & = 1 \cr x_3 & = 2 }\right. $

Svar 2.3:4

a)    $ax^2-ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.
b)    $ax^2-2ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.
c)    $ax^2-(3+\sqrt{3}\,)ax+3\sqrt{3}\,a=0\,$, där $\,a\ne 0\,$ är en konstant.

Svar 2.3:5

a)    Exempelvis $\ x^2+14x+49=0\,$.
b)    $3< x<4$
c)    $b=-5$

Svar 2.3:6

a)    $0$ b)    $-2$ c)    $\displaystyle \frac{3}{4}$

Svar 2.3:7

a)    $1$ b)    $\displaystyle -\frac{7}{4}$ c)    saknar max

Svar 2.3:8

Se lösningen i webmaterialet när du loggat in till kursen.

Svar 2.3:9

a)    $(-1,0)\ $ och $\ (1,0)$ b)    $(2,0)\ $ och $\ (3,0)$ c)    $(1,0)\ $ och $\ (3,0)$

Svar 2.3:10

Se lösningen i webmaterialet när du loggat in till kursen

Svar 3.1:1

a)    $2^{1/2}$ b)    $7^{5/2}$ c)    $3^{4/3}$ d)    $3^{1/4}$

Svar 3.1:2

a)    $3$ b)    $3$ c)    ej definierad d)    $5^{11/6}$
e)    $12$ f)    $2$ g)    $-5$

Svar 3.1:3

a)    $3$ b)    $\displaystyle \frac{4\sqrt{3}}{3}$
c)    $2\sqrt{5}$ d)    $2-\sqrt{2}$

Svar 3.1:4

a)    $0{,}4$ b)    $0{,}3$
c)    $-4\sqrt{2}$ d)    $2\sqrt{3}$

Svar 3.1:5

a)    $\displaystyle \frac{\sqrt{3}}{3}$ b)    $\displaystyle \frac{7^{2/3}}{7}$ c)    $3-\sqrt{7}$ d)    $\displaystyle \frac{\sqrt{17}+\sqrt{13}}{4}$

Svar 3.1:6

a)    $6+2\sqrt{2}+3\sqrt{5}+\sqrt{10}$ b)    $-\displaystyle \frac{5+4\sqrt{3}}{23}$
c)    $\displaystyle \frac{2}{3}\sqrt{6}+\displaystyle \frac{2}{3}\sqrt{3}-\displaystyle \frac{2}{5}\sqrt{10}-\displaystyle \frac{2}{5}\sqrt{5}$ d)    $\displaystyle \frac{5\sqrt{3}+7\sqrt{2}-\sqrt{6}-12}{23}$

Svar 3.1:7

a)    $\sqrt{5}-\sqrt{7}$ b)    $-\sqrt{35}$ c)    $\sqrt{17}$

Svar 3.1:8

a)    $\sqrt[\scriptstyle3]6 > \sqrt[\scriptstyle3]5$ b)    $7 > \sqrt7$
c)    $\sqrt7 > 2{,}5$ d)    $\sqrt[\scriptstyle3]2\cdot3 > \sqrt2\bigl(\sqrt[\scriptstyle4]3\,\bigr)^3$

Svar 3.2:1

$x=5$

Svar 3.2:2

$x=1$

Svar 3.2:3

$\left \{ \eqalign{ x_1 & = 3 \cr x_2 & = 4\cr } \right.$

Svar 3.2:4

Saknar lösning.

Svar 3.2:5

$x=1$

Svar 3.2:6

$x=\displaystyle\frac{5}{4}$

Svar 3.3:1

a)    $x=3$ b)    $x=-1$
c)    $x=-2$ d)    $x=4$

Svar 3.3:2

a)    $-1$ b)    $4$ c)    $-3$ d)    $0$
e)    $2$ f)    $3$ g)    $10$ h)    $-2$

Svar 3.3:3

a)    $3$ b)    $-\displaystyle \frac{1}{2}$ c)    $-3$
d)    $\displaystyle \frac{7}{3}$ e)    $4$ f)    $-2$
g)    $1$ h)    $\displaystyle \frac{5}{2}$

Svar 3.3:4

a)    $1$ b)    $0$ c)    $-\displaystyle \frac{1}{2}\lg{3}$

Svar 3.3:5

a)    $5$ b)    $0$ c)    $0$
d)    $0$ e)    $-2$ f)    $e^2$

Svar 3.3:6

a)    $1{,}262$
b)    $1{,}663$
c)    $4{,}762$

Svar 3.4:1

a)    $x=\ln 13$ b)    $x=\displaystyle\frac{\ln 2 - \ln 13}{1+\ln 3}$ c)    $x=\displaystyle\frac{\ln 7 - \ln 3}{1-\ln 2}$

Svar 3.4:2

a)    $ \left\{ \eqalign{ x_1&=\sqrt2 \cr x_2&=-\sqrt2 } \right. $ b)    $x=\ln \left(\displaystyle\frac{\sqrt17}{2}-\frac{1}{2}\right)$ c)    Saknar lösning

Svar 3.4:3

a)    $x=-\,\displaystyle\frac{1}{\ln{2}}\pm\sqrt{\left(\displaystyle\frac{1}{\ln{2}}\right)^2-1}$ b)    $x=\displaystyle \frac{5}{2}$
c)    $x=1$

Svar 4.1:1

a)    $90^\circ\ $ och $\ \displaystyle \frac{\pi}{2} \textrm{ rad} $ b)    $135^\circ\ $ och $\ \displaystyle \frac{3\pi}{4} \textrm{ rad}$
c)    $-240^\circ\ $ och $\ \displaystyle -\frac{4\pi}{3} \textrm{ rad}$ d)    $2910^\circ\ $ och $\ \displaystyle \frac{97\pi}{6} \textrm{ rad}$

Svar 4.1:2

a)    $\displaystyle \frac{\pi}{4}\textrm{ rad}$ b)    $\displaystyle \frac{3\pi}{4}\textrm{ rad}$ c)    $-\displaystyle \frac{7\pi}{20}\textrm{ rad}$ d)    $\displaystyle \frac{3\pi}{2}\textrm{ rad}$

Svar 4.1:3

a)    $x=50$ b)    $x=5$ c)    $x=15$

Svar 4.1:4

a)    $5 \textrm{ l.e.}$
b)    $\sqrt{61} \textrm{ l.e.}$
c)    $(2,0)$

Svar 4.1:5

a)    $(x-1)^2+(y-2)^2=4$
b)    $(x-2)^2+(y+1)^2=13$

Svar 4.1:6

a)    En cirkel med radie 3 och medelpunkt i origo. b)    En cirkel med radie $\sqrt 3$ och medelpunkt i punkten (1, 2).
c)    En cirkel med radie $\frac{1}{3}\sqrt 10$ och medelpunkt i punkten (1/3, -7/3).

Svar 4.1:7

a)    En cirkel med medelpunkt (-1, 1) och radie $\sqrt 3$. b)    En cirkel med medelpunkt (0, -2) och radie 2.
c)    En cirkel med medelpunkt (1, -3) och radie $\sqrt 7$.
d)    Endast punkten (1, -1).

Svar 4.1:8

$\displaystyle \frac{10}{\pi}\textrm{ varv }\approx 3,2 \textrm{ varv} $

Svar 4.1:9

$\displaystyle \frac{32\pi}{3} \textrm{ cm}^2 \approx 33,5 \textrm{ cm}^2$

Svar 4.1:10

$x=9$ dm

Svar 4.2:1

Facit till alla delfrågor

a)    $x=13\cdot\tan {27 ^\circ} \approx 6{,}62$ b)    $x=25\cdot\cos {32 ^\circ} \approx 21{,}2$
c)    $x=\displaystyle\frac{14}{\tan {40 ^\circ}} \approx 16{,}7$ d)    $x=\displaystyle\frac{16}{\cos {20 ^\circ}} \approx 17{,}0$
e)    $x=\displaystyle\frac{11}{\sin {35 ^\circ}} \approx 19{,}2$ f)    $x=\displaystyle\frac{19}{\tan {50 ^\circ}} \approx 15{,}9$

Svar 4.2:2

a)    $\tan v=\displaystyle\frac{2}{5}$ b)    $\sin v=\displaystyle\frac{7}{11}$
c)    $\cos v=\displaystyle\frac{5}{7}$ d)    $\sin v=\displaystyle\frac{3}{5}$
e)    $v=30 ^\circ$ f)    $\sin \displaystyle\frac{v}{2}=\displaystyle\frac{1}{3}$

Svar 4.2:3

a)    $-1$ b)    $1$ c)    $0$
d)    $0$ e)    $\displaystyle \frac{1}{\sqrt{2}}$ f)    $\displaystyle \frac{\sqrt{3}}{2}$

Svar 4.2:4

a)    $\displaystyle \frac{\sqrt{3}}{2}$ b)    $\displaystyle \frac{1}{2}$ c)    $-1$
d)    $0$ e)    $\displaystyle \frac{1}{\sqrt{3}}$ f)    $\sqrt{3}$

Svar 4.2:5

a)    $-\displaystyle \frac{1}{\sqrt{2}}$ b)    $1$ c)    $\displaystyle \frac{\sqrt{3}}{2}$ d)    $-1$

Svar 4.2:6

$x= \sqrt{3}-1$

Svar 4.2:7

Älvens bredd är $\ \displaystyle\frac{100}{\sqrt{3}-1}$ m $\approx 136{,}6$ m.


Svar 4.2:8

$\ell\cos \gamma=a \cos \alpha - b\cos \beta $

Svar 4.2:9

Avståndet är $\ \sqrt{205-48\sqrt{3}} \approx 11{,}0$ km.

Svar 4.3:1

a)    $v = \displaystyle \frac{9\pi}{5}$ b)    $v = \displaystyle \frac{6\pi}{7}$ c)    $v = \displaystyle \frac{9\pi}{7}$

Svar 4.3:2

a)    $v=\displaystyle \frac{\pi}{2}$ b)    $v=\displaystyle \frac{3\pi}{5}$

Svar 4.3:3

a)    $-a$ b)    $a$
c)    $\sqrt{1-a^2}$ d)    $\sqrt{1-a^2}$
e)    $-a$ f)    $\displaystyle \frac{\sqrt{3}}{2}\sqrt{1-a^2}+\displaystyle \frac{1}{2}\cdot a $

Svar 4.3:4

a)    $1-b^2$ b)    $\sqrt{1-b^2}$
c)    $2b\sqrt{1-b^2}$ d)    $2b^2-1$
e)    $\sqrt{1-b^2}\cdot\displaystyle \frac{1}{\sqrt{2}} + b\cdot \displaystyle \frac{1}{\sqrt{2}} $ f)    $b\cdot\displaystyle \frac{1}{2}+\sqrt{1-b^2}\cdot\displaystyle \frac{\sqrt{3}}{2}$

Svar 4.3:5

$\cos{v}=\displaystyle \frac{2\sqrt{6}}{7}\quad$ och $\quad\tan{v}=\displaystyle \frac{5}{2\sqrt{6}}\,$.

Svar 4.3:6

a)    $\sin{v}=-\displaystyle \frac{\sqrt{7}}{4}\quad$ och $\quad\tan{v}=-\displaystyle \frac{\sqrt{7}}{3}\,$.
b)    $\cos{v}=-\displaystyle \frac{\sqrt{91}}{10}\quad$ och $\quad\tan{v}=-\displaystyle \frac{3}{\sqrt{91}}\,$.
c)    $\sin{v}=-\displaystyle \frac{3}{\sqrt{10}}\quad$ och $\quad\cos{v}=-\displaystyle \frac{1}{\sqrt{10}}\,$.

Svar 4.3:7

a)    $\sin{(x+y)}=\displaystyle \frac{4\sqrt{2}+\sqrt{5}}{9}$
b)    $\sin{(x+y)}=\displaystyle \frac{3\sqrt{21}+8}{25}$

Svar 4.3:8

Se lösningen i webmaterialet när du loggat in till kursen

Svar 4.3:9

Se lösningen i webmaterialet när du loggat in till kursen

Svar 4.4:1

a)    $\displaystyle v=\frac{\pi}{6}\,$, $\,\displaystyle v=\frac{5\pi}{6}$ b)    $\displaystyle v=\frac{\pi}{3}\,$, $\,\displaystyle v=\frac{5\pi}{3}$
c)    $\displaystyle v=\frac{\pi}{2}$ d)    $\displaystyle v=\frac{\pi}{4}\,$, $\,\displaystyle v=\frac{5\pi}{4}$
e)    lösning saknas f)    $\displaystyle v=\frac{11\pi}{6}\,$, $\,\displaystyle v=\frac{7\pi}{6}$
g)    $\displaystyle v=\frac{5\pi}{6}\,$, $\,\displaystyle v=\frac{11\pi}{6}$

Svar 4.4:2

a)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{3}+2n\pi\cr x&=\displaystyle\frac{2\pi}{3}+2n\pi } \right.$

b)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{3}+2n\pi\cr x&=\displaystyle\frac{5\pi}{3}+2n\pi } \right.$

c)    $x=n\pi$
d)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{20}+\displaystyle\frac{2n\pi}{5}\cr x&=\displaystyle\frac{3\pi}{20}+\displaystyle\frac{2n\pi}{5} } \right.$

e)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{30}+\displaystyle\frac{2n\pi}{5}\cr x&=\displaystyle\frac{\pi}{6}+\displaystyle\frac{2n\pi}{5}} \right.$

f)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{4}+\displaystyle\frac{2n\pi}{3}\cr x&=\displaystyle\frac{5\pi}{12}+\displaystyle\frac{2n\pi}{3}} \right.$

Svar 4.4:3

a)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{6}+2n\pi\cr x&=\displaystyle\frac{11\pi}{6}+2n\pi }\right.$

b)   

$\left\{\eqalign{ x&=\displaystyle\frac{\pi}{5}+2n\pi\cr x&=\displaystyle\frac{4\pi}{5}+2n\pi }\right.$

c)   

$\left\{\eqalign{ x&=25^\circ + n\cdot 360^\circ\cr x&=75^\circ + n\cdot 360^\circ }\right.$

d)   

$\left\{\eqalign{ x&=5^\circ + n \cdot 120^\circ \cr x&= 55^\circ + n \cdot 120^\circ }\right.$

Svar 4.4:4

$v_1=50^\circ$, $\ \ v_2=120^\circ$, $\ \ v_3=230^\circ\ \ $ och $\ \ v_4=300^\circ$

Svar 4.4:5

a)   

$\left\{\eqalign{ x&=n\pi\cr x&=\displaystyle \frac{\pi}{4}+\displaystyle \frac{n\pi}{2} }\right.$

b)    $x=\displaystyle \frac{n\pi}{3}$ c)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{20}+\displaystyle \frac{n\pi}{2}\cr x&=-\displaystyle \frac{\pi}{30}+\displaystyle \frac{n\pi}{3} }\right.$

Svar 4.4:6

a)   

$x=n\pi$

b)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{4}+2n\pi\cr x&=\displaystyle \frac{\pi}{2}+n\pi\cr x&=\displaystyle \frac{3\pi}{4}+2n\pi}\right.$

c)   

$\left\{\eqalign{ x&=\displaystyle \frac{2n\pi}{3}\cr x&=\displaystyle \pi + 2n\pi\cr }\right.$

Svar 4.4:7

a)   

$\left\{ \matrix{ x=\displaystyle \frac{\pi}{6}+2n\pi\cr x=\displaystyle \frac{5\pi}{6}+2n\pi\cr x=\displaystyle \frac{3\pi}{2}+2n\pi }\right.$

b)    $x=\pm \displaystyle \frac{\pi}{3} + 2n\pi $ c)   

$\left\{ \matrix{ x=\displaystyle \frac{\pi}{2}+2n\pi\cr x=\displaystyle \frac{\pi}{14}+\displaystyle \frac{2n\pi}{7} }\right.$

Svar 4.4:8

a)   

$\left\{\eqalign{ x&=\displaystyle \frac{\pi}{4}+2n\pi\cr x&=\displaystyle \frac{\pi}{2}+n\pi\cr x&=\displaystyle \frac{3\pi}{4}+2n\pi }\right.$

b)    $x=\displaystyle \frac{\pi}{3}+n\pi$ c)   

$\left\{\eqalign{ x&=n\pi\cr x&=\displaystyle \frac{3\pi}{4}+n\pi }\right.$












































































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