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3.3 Övningar

Sommarmatte 1

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Versionen från 29 april 2007 kl. 13.15 (redigera)
Ossiang (Diskussion | bidrag)
(Övning 3.3:6)
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Nuvarande version (31 maj 2007 kl. 07.02) (redigera) (ogör)
KTH.SE:u1rp004j (Diskussion | bidrag)

 
(8 mellanliggande versioner visas inte.)
Rad 1: Rad 1:
 +
==Övning 3.3:1== ==Övning 3.3:1==
<div class="ovning"> <div class="ovning">
-Best&auml;m x om+Best&auml;m $\,x\,$ om
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">10^x=1\,000</td>+<td class="ntext" width="50%">10^x=1\,000</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">10^x=0,1</td>+<td class="ntext" width="50%">$10^x=0{,}1$</td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">\displaystyle \frac{1}{10^x}=100</td>+<td class="ntext" width="50%">\displaystyle \frac{1}{10^x}=100</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">\displaystyle \frac{1}{10^x}=0,000\,1</td>+<td class="ntext" width="50%">$\displaystyle \frac{1}{10^x}=0{,}000\,1$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 21: Rad 23:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">x=3</td>+<td class="ntext" width="50%">x=3</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">x=-1</td>+<td class="ntext" width="50%">x=-1</td>
 +</tr>
 +<tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">x=-2</td>+<td class="ntext" width="50%">x=-2</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">x=4</td>+<td class="ntext" width="50%">x=4</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 40: Rad 43:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:3_3_1a.gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_1a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 48: Rad 58:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:3_3_1b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_1b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 56: Rad 73:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:3_3_1c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_1c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 64: Rad 88:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br \>[[Bild:3_3_1d.gif]]+Lösning till delfråga d)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_1d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 75: Rad 106:
Ber&auml;kna Ber&auml;kna
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">\lg{ 0,1}</td>+<td class="ntext" width="25%">$\lg{ 0{,}1}$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">\lg{ 10\,000}</td>+<td class="ntext" width="25%">\lg{ 10\,000}</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">\lg {0,001}</td>+<td class="ntext" width="25%">$\lg {0{,}001}$</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">\lg {1}</td>+<td class="ntext" width="25%">\lg {1}</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">e)</td> <td class="ntext">e)</td>
-<td class="ntext">10^{\lg{2}}</td>+<td class="ntext" width="25%">10^{\lg{2}}</td>
<td class="ntext">f)</td> <td class="ntext">f)</td>
-<td class="ntext">\lg{10^3}</td>+<td class="ntext" width="25%">\lg{10^3}</td>
<td class="ntext">g)</td> <td class="ntext">g)</td>
-<td class="ntext">10^{-\lg{0,1}}</td>+<td class="ntext" width="25%">$10^{-\lg{0{,}1}}$</td>
<td class="ntext">h)</td> <td class="ntext">h)</td>
-<td class="ntext">\lg{\displaystyle \frac{1}{10^2}}</td>+<td class="ntext" width="25%">\lg{\displaystyle \frac{1}{10^2}}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
</table> </table>
- 
</div> </div>
Rad 105: Rad 133:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">-1</td>+<td class="ntext" width="25%">-1</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">4</td>+<td class="ntext" width="25%">4</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">-3</td>+<td class="ntext" width="25%">-3</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">0</td>+<td class="ntext" width="25%">0</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">e)</td> <td class="ntext">e)</td>
-<td class="ntext">2</td>+<td class="ntext" width="25%">2</td>
<td class="ntext">f)</td> <td class="ntext">f)</td>
-<td class="ntext">3</td>+<td class="ntext" width="25%">3</td>
<td class="ntext">g)</td> <td class="ntext">g)</td>
-<td class="ntext">10</td>+<td class="ntext" width="25%">10</td>
<td class="ntext">h)</td> <td class="ntext">h)</td>
-<td class="ntext">-2</td>+<td class="ntext" width="25%">-2</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 135: Rad 161:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:3_3_2a.gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_2a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:3_3_2b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_2b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:3_3_2c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_2c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br \>[[Bild:3_3_2d.gif]]+Lösning till delfråga d)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_2d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e<br \>[[Bild:3_3_2e.gif]]+Lösning till delfråga e)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_2e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga f<br \>[[Bild:3_3_2f.gif]]+Lösning till delfråga f)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_2f.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning g&nbsp;</div>+<div class=NavHead>L&ouml;sning g)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga g<br \>[[Bild:3_3_2g.gif]]+Lösning till delfråga g)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_2g.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning h&nbsp;</div>+<div class=NavHead>L&ouml;sning h)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga h<br \>[[Bild:3_3_2h.gif]]+Lösning till delfråga h)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_2h.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 202: Rad 277:
Ber&auml;kna Ber&auml;kna
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">\log_2{8}</td>+<td class="ntext" width="33%">\log_2{8}</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">\log_9{\displaystyle \frac{1}{3}}</td>+<td class="ntext" width="33%">\log_9{\displaystyle \frac{1}{3}}</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">\log_2{0,125}</td>+<td class="ntext" width="33%">$\log_2{0{,}125}$</td>
-<td class="ntext">d)</td>+
-<td class="ntext">$\log_3{\left(9\cdot3^{1/3}\right)}$</td>+
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
 +<td class="ntext">d)</td>
 +<td class="ntext" width="33%">\log_3{\left(9\cdot3^{1/3}\right)}</td>
<td class="ntext">e)</td> <td class="ntext">e)</td>
-<td class="ntext">2^{\log_{\scriptstyle2}{4}}</td>+<td class="ntext" width="33%">2^{\log_{\scriptstyle2}{4}}</td>
<td class="ntext">f)</td> <td class="ntext">f)</td>
-<td class="ntext">\log_2{4}+\log_2{\displaystyle \frac{1}{16}}</td>+<td class="ntext" width="33%">\log_2{4}+\log_2{\displaystyle \frac{1}{16}}</td>
 +</tr>
 +<tr align="left">
<td class="ntext">g)</td> <td class="ntext">g)</td>
-<td class="ntext">\log_3{12}-\log_3{4}</td>+<td class="ntext" width="33%">\log_3{12}-\log_3{4}</td>
<td class="ntext">h)</td> <td class="ntext">h)</td>
-<td class="ntext">$\log_a{\left(a^2\sqrt{a}\right)}$</td>+<td class="ntext" width="33%">$\log_a{\bigl(a^2\sqrt{a}\,\bigr)}$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 231: Rad 306:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">3</td>+<td class="ntext" width="33%">3</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">-\displaystyle \frac{1}{2}</td>+<td class="ntext" width="33%">-\displaystyle \frac{1}{2}</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">-3</td>+<td class="ntext" width="33%">$-3$</td>
-<td class="ntext">d)</td>+
-<td class="ntext">$\displaystyle \frac{7}{3}$</td>+
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
 +<td class="ntext">d)</td>
 +<td class="ntext" width="33%">\displaystyle \frac{7}{3}</td>
<td class="ntext">e)</td> <td class="ntext">e)</td>
-<td class="ntext">4</td>+<td class="ntext" width="33%">4</td>
<td class="ntext">f)</td> <td class="ntext">f)</td>
-<td class="ntext">-2</td>+<td class="ntext" width="33%">-2</td>
 +</tr>
 +<tr align="left">
<td class="ntext">g)</td> <td class="ntext">g)</td>
-<td class="ntext">1</td>+<td class="ntext" width="33%">1</td>
<td class="ntext">h)</td> <td class="ntext">h)</td>
-<td class="ntext">\displaystyle \frac{5}{2}</td>+<td class="ntext" width="33%">\displaystyle \frac{5}{2}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 261: Rad 336:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:3_3_3a.gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_3a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:3_3_3b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_3b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:3_3_3c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_3c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br \>[[Bild:3_3_3d.gif]]+Lösning till delfråga d)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_3d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e<br \>[[Bild:3_3_3e.gif]]+Lösning till delfråga e)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_3e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga f<br \>[[Bild:3_3_3f.gif]]+Lösning till delfråga f)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_3f.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning g&nbsp;</div>+<div class=NavHead>L&ouml;sning g)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga g<br \>[[Bild:3_3_3g.gif]]+Lösning till delfråga g)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_3g.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning h&nbsp;</div>+<div class=NavHead>L&ouml;sning h)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga h<br \>[[Bild:3_3_3h.gif]]+Lösning till delfråga h)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_3h.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 328: Rad 452:
F&ouml;renkla F&ouml;renkla
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">\lg{50}-\lg{5}</td>+<td class="ntext" width="33%">\lg{50}-\lg{5}</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">\lg{23}+\lg{\displaystyle \frac{1}{23}}</td>+<td class="ntext" width="33%">\lg{23}+\lg{\displaystyle \frac{1}{23}}</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">\lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}</td>+<td class="ntext" width="33%">\lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 344: Rad 467:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">1</td>+<td class="ntext" width="33%">1</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">0</td>+<td class="ntext" width="33%">0</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">-\displaystyle \frac{1}{2}\lg{3}</td>+<td class="ntext" width="33%">-\displaystyle \frac{1}{2}\lg{3}</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 361: Rad 483:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:3_3_4a.gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_4a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:3_3_4b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_4b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:3_3_4c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_4c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 386: Rad 529:
F&ouml;renkla F&ouml;renkla
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">\ln{e^3}+\ln{e^2}</td>+<td class="ntext" width="33%">\ln{e^3}+\ln{e^2}</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">\ln{8}-\ln{4}-\ln{2}</td>+<td class="ntext" width="33%">\ln{8}-\ln{4}-\ln{2}</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">(\ln{1})\cdot e^2</td>+<td class="ntext" width="33%">(\ln{1})\cdot e^2</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">\ln{e}-1</td>+<td class="ntext" width="33%">\ln{e}-1</td>
<td class="ntext">e)</td> <td class="ntext">e)</td>
-<td class="ntext">\ln{\displaystyle \frac{1}{e^2}}</td>+<td class="ntext" width="33%">\ln{\displaystyle \frac{1}{e^2}}</td>
<td class="ntext">f)</td> <td class="ntext">f)</td>
-<td class="ntext">\left(e^{\ln{e}}\right)^2</td>+<td class="ntext" width="33%">\left(e^{\ln{e}}\right)^2</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 411: Rad 552:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">5</td>+<td class="ntext" width="33%">5</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">0</td>+<td class="ntext" width="33%">0</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">0</td>+<td class="ntext" width="33%">0</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">0</td>+<td class="ntext" width="33%">0</td>
<td class="ntext">e)</td> <td class="ntext">e)</td>
-<td class="ntext">-2</td>+<td class="ntext" width="33%">-2</td>
<td class="ntext">f)</td> <td class="ntext">f)</td>
-<td class="ntext">e^2</td>+<td class="ntext" width="33%">e^2</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 437: Rad 576:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:3_3_5a.gif]]+Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_5a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:3_3_5b.gif]]+Lösning till delfråga b)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_5b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:3_3_5c.gif]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_5c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br \>[[Bild:3_3_5d.gif]]+Lösning till delfråga d)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_5d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e<br \>[[Bild:3_3_5e.gif]]+Lösning till delfråga e)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_5e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga f<br \>[[Bild:3_3_5f.gif]]+Lösning till delfråga f)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_5f.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 480: Rad 661:
==&Ouml;vning 3.3:6== ==&Ouml;vning 3.3:6==
-<div class="ovning"><table width="100%" cellspacing="10px">+<div class="ovning">
-<tr>+[[Bild:miniraknare.gif||right]]
-<td>+Anv&auml;nd minir&auml;knaren till h&ouml;ger f&ouml;r att ber&auml;kna med tre decimaler (Knappen <tt>LN</tt> betecknar den naturliga logaritmen i basen ''e''):
 +<table width="100%" cellspacing="10px">
 +<tr align="left"><td height="5px"/></tr>
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="100%">\log_3{4}</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">b)</td>
 +<td class="ntext" width="100%">\lg{46}</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">c)</td>
 +<td class="ntext" width="100%">\log_3{\log_2{(3^{118})}}</td>
 +</tr>
 +<tr align="left"><td height="40px"/></tr>
 +</table>
 +</div>
-Anv&auml;nd minir&auml;knaren till h&ouml;ger f&ouml;r att ber&auml;kna med tre decimaler. (Knappen <tt>LN</tt> betecknar den naturliga logaritmen i basen ''e''.)+<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>Facit&nbsp;</div>
 +<div class=NavContent>
 +Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"><td height="5px"/></tr> <tr align="left"><td height="5px"/></tr>
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">$\log_3{4}$</td>+<td class="ntext" width="100%">$1{,}262$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$\lg{46}$</td>+<td class="ntext" width="100%">$1{,}663$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">$\log_3{\log_2{(3^{118})}}$</td>+<td class="ntext" width="100%">$4{,}762$</td>
</tr> </tr>
<tr align="left"><td height="5px"/></tr> <tr align="left"><td height="5px"/></tr>
-</table></td>+</table>
-<td>+
-<!-- Miniräknare -->+
-<div>+
-<form onsubmit="keyclick('='); return false;">+
-<div id="calculator" class="drag">+
-<div class="calculatorcontainer">+
-<input type="text" name="input" size="16" id="result" value="0"+
-onclick="this.focus()" onkeyup="addToCalcDirect(this.value)">+
-<br/>+
-<input type="button" value="AC" onclick="keyclick(this.value)"><input type="button" value="C" onclick="keyclick(this.value)"><input type="button" value="LN" onclick="keyclick(this.value)"><input type="button" value="×" onclick="keyclick(this.value)"><br/>+
-<input type="button" value="7" onclick="keyclick(this.value)"><input type="button" value="8" onclick="keyclick(this.value)"><input type="button" value="9" onclick="keyclick(this.value)"><input type="button" value="÷" onclick="keyclick(this.value)"><br/>+
-<input type="button" value="4" onclick="keyclick(this.value)"><input type="button" value="5" onclick="keyclick(this.value)"><input type="button" value="6" onclick="keyclick(this.value)"><input type="button" value="+" onclick="keyclick(this.value)"><br/>+
-<input type="button" value="1" onclick="keyclick(this.value)"><input type="button" value="2" onclick="keyclick(this.value)"><input type="button" value="3" onclick="keyclick(this.value)"><input type="button" value="-" onclick="keyclick(this.value)"><br/>+
-<input type="button" value="+/-" onclick="keyclick(this.value)"><input type="button" value="0" onclick="keyclick(this.value)"><input type="button" value="." onclick="keyclick(this.value)"><input type="button" value="=" onclick="keyclick(this.value)">+
</div> </div>
</div> </div>
-</form>+ 
-</div>+<div class=NavFrame style="CLEAR: both">
-<!-- Slut miniräknare -->+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_6a-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:3_3_6a-2(2).gif]]
</td> </td>
</tr> </tr>
</table> </table>
 +</div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>Facit&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Lösning till delfråga b)
- +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_6b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning &nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga <br \>[[Bild:]]+Lösning till delfråga c)
 +<table width="100%">
 +<tr>
 +<td align="center">
 +[[Bild:3_3_6c-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:3_3_6c-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>

Nuvarande version

Innehåll

[göm]

[redigera] Övning 3.3:1

Bestäm \,x\, om

a) 10^x=1\,000 b) 10^x=0{,}1
c) \displaystyle \frac{1}{10^x}=100 d) \displaystyle \frac{1}{10^x}=0{,}000\,1




[redigera] Övning 3.3:2

Beräkna

a) \lg{ 0{,}1} b) \lg{ 10\,000} c) \lg {0{,}001} d) \lg {1}
e) 10^{\lg{2}} f) \lg{10^3} g) 10^{-\lg{0{,}1}} h) \lg{\displaystyle \frac{1}{10^2}}

[redigera] Övning 3.3:3

Beräkna

a) \log_2{8} b) \log_9{\displaystyle \frac{1}{3}} c) \log_2{0{,}125}
d) \log_3{\left(9\cdot3^{1/3}\right)} e) 2^{\log_{\scriptstyle2}{4}} f) \log_2{4}+\log_2{\displaystyle \frac{1}{16}}
g) \log_3{12}-\log_3{4} h) \log_a{\bigl(a^2\sqrt{a}\,\bigr)}

[redigera] Övning 3.3:4

Förenkla

a) \lg{50}-\lg{5} b) \lg{23}+\lg{\displaystyle \frac{1}{23}} c) \lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}

[redigera] Övning 3.3:5

Förenkla

a) \ln{e^3}+\ln{e^2} b) \ln{8}-\ln{4}-\ln{2} c) (\ln{1})\cdot e^2
d) \ln{e}-1 e) \ln{\displaystyle \frac{1}{e^2}} f) \left(e^{\ln{e}}\right)^2

[redigera] Övning 3.3:6

Använd miniräknaren till höger för att beräkna med tre decimaler (Knappen LN betecknar den naturliga logaritmen i basen e):

a) \log_3{4}
b) \lg{46}
c) \log_3{\log_2{(3^{118})}}
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