http://wiki.math.se/wikis/sf0600_0701/index.php?action=history&feed=atom&title=%C3%96vningar_2.2
Övningar 2.2 - Versionshistorik
2026-04-24T21:08:51Z
Versionshistorik för denna sida på wikin
MediaWiki 1.9.3
http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vningar_2.2&diff=2437&oldid=prev
KTH.SE:u1zpa8nw den 17 juli 2007 kl. 09.40
2007-07-17T09:40:09Z
<p></p>
<table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;">
<tr>
<td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td>
<td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 17 juli 2007 kl. 09.40</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 181:</strong></td>
<td colspan="2" align="left"><strong>Rad 181:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></table></td><td> </td><td style="background: #eee; font-size: smaller;"></table></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></div></td><td> </td><td style="background: #eee; font-size: smaller;"></div></td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr>
<tr><td colspan="2"> </td><td>+</td><td style="background: #cfc; font-size: smaller;"><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></td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vningar_2.2&diff=2292&oldid=prev
KTH.SE:u1zpa8nw den 16 juli 2007 kl. 10.47
2007-07-16T10:47:49Z
<p></p>
<a href="http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vningar_2.2&diff=2292&oldid=2238">(Skillnad mellan versioner)</a>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vningar_2.2&diff=2238&oldid=prev
KTH.SE:u1zpa8nw: Ny sida: __NOTOC__ ==Övning 2.2:1== <div class="ovning"> Lös ekvationerna <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="50%">$x-2...
2007-07-16T07:59:52Z
<p>Ny sida: __NOTOC__ ==Övning 2.2:1== <div class="ovning"> L&ouml;s ekvationerna <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="50%">$x-2...</p>
<p><b>Ny sida</b></p><div>__NOTOC__<br />
==Övning 2.2:1==<br />
<div class="ovning"><br />
L&ouml;s ekvationerna<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$x-2=-1$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$2x+1=13$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\displaystyle\frac{1}{3}x-1=x$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$5x+7=2x-6$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 2.2:2==<br />
<div class="ovning"><br />
L&ouml;s ekvationerna<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\displaystyle\frac{5x}{6}-\displaystyle\frac{x+2}{9}=\displaystyle\frac{1}{2}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle\frac{8x+3}{7}-\displaystyle\frac{5x-7}{4}=2$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$(x+3)^2-(x-5)^2=6x+4$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$(x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 2.2:3==<br />
<div class="ovning"><br />
L&ouml;s ekvationerna<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">$\displaystyle\frac{x+3}{x-3}-\displaystyle\frac{x+5}{x-2}=0$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">$\displaystyle\frac{4x}{4x-7}-\displaystyle\frac{1}{2x-3}=1$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">$\left(\displaystyle\frac{1}{x-1}-\frac{1}{x+1}\right)\left(x^2+\frac{1}{2}\right)=\displaystyle\frac{6x-1}{3x-3}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d) </td><br />
<td class="ntext" width="100%"> $\left(\displaystyle\frac{2}{x}-3\right)\left(\displaystyle\frac{1}{4x}+\frac{1}{2}\right)-\left(\displaystyle\frac{1}{2x}-\frac{2}{3}\right)^2-\left(\displaystyle\frac{1}{2x}+\frac{1}{3}\right)\left(\displaystyle\frac{1}{2x}-\frac{1}{3}\right)=0$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.2:4==<br />
<div class="ovning"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td>a)</td><br />
<td width="100%">Skriv ekvationen f&ouml;r linjen $\,y=2x+3\,$ på formen $\,ax+by=c\,$.</td><br />
</tr><br />
<tr align="left"><br />
<td>b)</td><br />
<td width="100%">Skriv ekvationen f&ouml;r linjen $\,3x+4y-5=0\,$ på formen $\,y=kx+m\,$.</td><br />
</tr><br />
<tr><td height="5px"\></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.2:5==<br />
<div class="ovning"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left" valign="top"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">Best&auml;m ekvationen f&ouml;r den r&auml;ta linje som g&aring;r genom punkterna $\,(2,3)\,$ och $\,(3,0)\,$.</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">Best&auml;m ekvationen f&ouml;r den r&auml;ta linje som har riktningskoefficient $\,-3\,$ och g&aring;r genom punkten $\,(1,-2)\,$.</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">Best&auml;m ekvationen f&ouml;r den r&auml;ta linje som g&aring;r genom punkten $\,(-1,2)\,$ och &auml;r parallell med linjen $\,y=3x+1\,$.</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="100%">Best&auml;m ekvationen f&ouml;r den r&auml;ta linje som g&aring;r genom punkten $\,(2,4)\,$ och &auml;r vinkelr&auml;t mot linjen $\,y=2x+5\,$.</td><br />
</tr><br />
<tr align="left" valign="top"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="100%">Best&auml;m riktningskoefficienten, $\,k\,$, f&ouml;r den r&auml;ta linje som sk&auml;r ''x''-axeln i punkten $\,(5,0)\,$ och ''y''-axeln i punkten $\,(0,-8)\,$.</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.2:6==<br />
<div class="ovning"><br />
Finn sk&auml;rningspunkten mellan f&ouml;ljande linjer<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$y=3x+5\ $ och ''x''-axeln</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$y=-x+5\ $ och ''y''-axeln</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$4x+5y+6=0\ $ och ''y''-axeln</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$x+y+1=0\ $ och $\ x=12$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="50%">$2x+y-1=0\ $ och $\ y-2x-2=0$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.2:7==<br />
<div class="ovning"><br />
Skissera grafen till f&ouml;ljande funktioner<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$f(x)=3x-2$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$f(x)=2-x$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$f(x)=2$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.2:8==<br />
<div class="ovning"><br />
Rita in i ett ''xy''-plan alla punkter vars koordinater $\,(x,y)\,$ uppfyller<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$y \geq x $</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$y &lt; 3x -4 $</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$2x+3y \leq 6 $</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.2:9==<br />
<div class="ovning"><br />
Ber&auml;kna arean av den triangel som <br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">har h&ouml;rn i punkterna $\,(1,4)\,$, $\,(3,3)\,$ och $\,(1,0)\,$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">begr&auml;nsas av linjerna $\ x=2y\,$, $\ y=4\ $ och $\ y=10-2x\,$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">beskrivs av olikheterna $\ x+y \geq -2\,$, $\ 2x-y \leq 2\ $ och $\ 2y-x \leq 2\,$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div></div>
KTH.SE:u1zpa8nw