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1.2 Övningar - Versionshistorik
2026-06-21T11:10:45Z
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KTH.SE:u1tyze7e: Korrekturläst
2007-06-18T07:40:56Z
<p>Korrekturläst</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 18 juni 2007 kl. 07.40</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 148:</strong></td>
<td colspan="2" align="left"><strong>Rad 148:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\ln \ln x$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\ln \ln x$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">e)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">e)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$(2x+1<span style="color: red; font-weight: bold;">)^2(1-x</span>)^4$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">x</span>(2x+1)^4$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos \sqrt{1-x}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos \sqrt{1-x}$</td></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 174:</strong></td>
<td colspan="2" align="left"><strong>Rad 174:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$(2x+1)^3(10x+1)$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$(2x+1)^3(10x+1)$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle<span style="color: red; font-weight: bold;">-</span>\frac{\sin\sqrt{1-x}}{2\sqrt{1-x}}$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle\frac{\sin\sqrt{1-x}}{2\sqrt{1-x}}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></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 colspan="2" align="left"><strong>Rad 297:</strong></td>
<td colspan="2" align="left"><strong>Rad 297:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle\frac{1}{2\sqrt{x}\sqrt{x+1}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle\frac{1}{2\sqrt{x}\sqrt{x+1}}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle\frac{1}{(x-1)^{3/2}}$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle <span style="color: red; font-weight: bold;">- </span>\frac{1}{(x-1)^{3/2<span style="color: red; font-weight: bold;">}\sqrt{x+1</span>}}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">c)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">c)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle - \frac{1-<span style="color: red; font-weight: bold;">x</span>^2}{x^2(1-x^2)^{3/2}}$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle - \frac{1-<span style="color: red; font-weight: bold;">2x</span>^2}{x^2(1-x^2)^{3/2}}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 307:</strong></td>
<td colspan="2" align="left"><strong>Rad 307:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$e^{\sin x^2}\cdot \cos x^2 \cdot 2x$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$e^{\sin x^2}\cdot \cos x^2 \cdot 2x$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">e</span>^{\tan <span style="color: red; font-weight: bold;">x \cdot \ln </span>x}\<span style="color: red; font-weight: bold;">left</span>(<span style="color: red; font-weight: bold;">\displaystyle</span>\frac{\ln x}{\cos^2x}+\frac{\tan x}{x}\<span style="color: red; font-weight: bold;">right</span>)$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">\displaystyle x</span>^{\tan x}\<span style="color: red; font-weight: bold;">Bigl</span>(\frac{\ln x}{\cos^2x}+\frac{\tan x}{x}\<span style="color: red; font-weight: bold;">Bigr</span>)$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></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>
</table>
KTH.SE:u1tyze7e
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=518&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:4 */
2007-06-08T08:10:10Z
<p><span class="autocomment">Övning 1.2:4</span></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 8 juni 2007 kl. 08.10</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 403:</strong></td>
<td colspan="2" align="left"><strong>Rad 403:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;">==Övning 1.2:4==</td><td> </td><td style="background: #eee; font-size: smaller;">==Övning 1.2:4==</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><div class="ovning"></td><td> </td><td style="background: #eee; font-size: smaller;"><div class="ovning"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">Beräkna <span style="color: red; font-weight: bold;">derivatan </span>av följande funktioner och förenkla svaret så långt som möjligt</td><td>+</td><td style="background: #cfc; font-size: smaller;">Beräkna <span style="color: red; font-weight: bold;">andraderivatan </span>av följande funktioner och förenkla svaret så långt som möjligt</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><table width="100%" cellspacing="10px"></td><td> </td><td style="background: #eee; font-size: smaller;"><table width="100%" cellspacing="10px"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=517&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:4 */
2007-06-08T08:06:12Z
<p><span class="autocomment">Övning 1.2:4</span></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 8 juni 2007 kl. 08.06</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 440:</strong></td>
<td colspan="2" align="left"><strong>Rad 440:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr></td><td> </td><td style="background: #eee; font-size: smaller;"><tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:1_2_4a.gif]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:1_2_4a<span style="color: red; font-weight: bold;">-1(2).gif]]<br\>[[Bild:1_2_4a-2(2)</span>.gif]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td></td><td> </td><td style="background: #eee; font-size: smaller;"></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 454:</strong></td>
<td colspan="2" align="left"><strong>Rad 454:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr></td><td> </td><td style="background: #eee; font-size: smaller;"><tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:1_2_4b.gif]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:1_2_4b<span style="color: red; font-weight: bold;">-1(2).gif]]<br\>[[Bild:1_2_4b-2(2)</span>.gif]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td></td><td> </td><td style="background: #eee; font-size: smaller;"></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=516&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:3 */
2007-06-08T08:04:46Z
<p><span class="autocomment">Övning 1.2:3</span></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 8 juni 2007 kl. 08.04</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 324:</strong></td>
<td colspan="2" align="left"><strong>Rad 324:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr></td><td> </td><td style="background: #eee; font-size: smaller;"><tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:1_2_3a.gif]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:1_2_3a<span style="color: red; font-weight: bold;">-1(2).gif]]<br\>[[Bild:1_2_3a-2(2)</span>.gif]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td></td><td> </td><td style="background: #eee; font-size: smaller;"></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 338:</strong></td>
<td colspan="2" align="left"><strong>Rad 338:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr></td><td> </td><td style="background: #eee; font-size: smaller;"><tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:1_2_3b.gif]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:1_2_3b<span style="color: red; font-weight: bold;">-1(2).gif]]<br\>[[Bild:1_2_3b-2(2)</span>.gif]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td></td><td> </td><td style="background: #eee; font-size: smaller;"></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 352:</strong></td>
<td colspan="2" align="left"><strong>Rad 352:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr></td><td> </td><td style="background: #eee; font-size: smaller;"><tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:1_2_3c.gif]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:1_2_3c<span style="color: red; font-weight: bold;">-1(2).gif]]<br\>[[Bild:1_2_3c-2(2)</span>.gif]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td></td><td> </td><td style="background: #eee; font-size: smaller;"></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=515&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:2 */
2007-06-08T08:01:41Z
<p><span class="autocomment">Övning 1.2:2</span></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 8 juni 2007 kl. 08.01</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 244:</strong></td>
<td colspan="2" align="left"><strong>Rad 244:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr></td><td> </td><td style="background: #eee; font-size: smaller;"><tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:1_2_2e.gif]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:1_2_2e<span style="color: red; font-weight: bold;">-1(2).gif]]<br\>[[Bild:1_2_2e-2(2)</span>.gif]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td></td><td> </td><td style="background: #eee; font-size: smaller;"></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td colspan="2" align="left"><strong>Rad 258:</strong></td>
<td colspan="2" align="left"><strong>Rad 258:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr></td><td> </td><td style="background: #eee; font-size: smaller;"><tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:1_2_2f.gif]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:1_2_2f<span style="color: red; font-weight: bold;">-1(2).gif]]<br\>[[Bild:1_2_2f-2(2)</span>.gif]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td></td><td> </td><td style="background: #eee; font-size: smaller;"></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=514&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:1 */
2007-06-08T08:00:22Z
<p><span class="autocomment">Övning 1.2:1</span></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 8 juni 2007 kl. 08.00</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 125:</strong></td>
<td colspan="2" align="left"><strong>Rad 125:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr></td><td> </td><td style="background: #eee; font-size: smaller;"><tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td><td> </td><td style="background: #eee; font-size: smaller;"><td align="center"></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;">[[Bild:1_2_1f.gif]]</td><td>+</td><td style="background: #cfc; font-size: smaller;">[[Bild:1_2_1f<span style="color: red; font-weight: bold;">-1(2).gif]]<br\>[[Bild:1_2_1f-2(2)</span>.gif]]</td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></td></td><td> </td><td style="background: #eee; font-size: smaller;"></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=445&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:4 */
2007-06-07T10:08:55Z
<p><span class="autocomment">Övning 1.2:4</span></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 7 juni 2007 kl. 10.08</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 421:</strong></td>
<td colspan="2" align="left"><strong>Rad 421:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">a)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">a)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">Svar</span></td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">$\displaystyle\frac{3x}{(1-x^2)^{5/2}}$</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">Svar</span></td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">$\displaystyle - \frac{2\sin \ln x}{x}$</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></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>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=444&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:3 */
2007-06-07T10:06:33Z
<p><span class="autocomment">Övning 1.2:3</span></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 7 juni 2007 kl. 10.06</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 295:</strong></td>
<td colspan="2" align="left"><strong>Rad 295:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">a)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">a)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle\frac{}{}$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle\frac{<span style="color: red; font-weight: bold;">1</span>}{<span style="color: red; font-weight: bold;">2\sqrt{x}\sqrt{x+1}</span>}$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">\displaystyle\frac{1}{(x-1)^{3/2}}</span>$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">c)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">c)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">\displaystyle - \frac{1-x^2}{x^2(1-x^2)^{3/2}}</span>$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">d)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">d)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">-\cos\cos\sin x \cdot \sin\sin x \cdot \cos x</span>$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">e)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">e)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">e^{\sin x^2}\cdot \cos x^2 \cdot 2x</span>$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">e^{\tan x \cdot \ln x}\left(\displaystyle\frac{\ln x}{\cos^2x}+\frac{\tan x}{x}\right)</span>$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></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>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=443&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:3 */
2007-06-07T09:59:20Z
<p><span class="autocomment">Övning 1.2:3</span></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 7 juni 2007 kl. 09.59</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 295:</strong></td>
<td colspan="2" align="left"><strong>Rad 295:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">a)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">a)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">Svar</span></td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">$\displaystyle\frac{}{}$</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">Svar</span></td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">$$</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">c)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">c)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">Svar</span></td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">$$</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td><td> </td><td style="background: #eee; font-size: smaller;"><tr align="left"></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">d)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">d)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">Svar</span></td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">$$</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">e)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">e)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">Svar</span></td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">$$</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">f)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">Svar</span></td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%"><span style="color: red; font-weight: bold;">$$</span></td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"></tr></td><td> </td><td style="background: #eee; font-size: smaller;"></tr></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>
</table>
KTH.SE:u1zpa8nw
http://wiki.math.se/wikis/sf0601_0701/index.php?title=1.2_%C3%96vningar&diff=442&oldid=prev
KTH.SE:u1zpa8nw: /* Övning 1.2:2 */
2007-06-07T09:57:43Z
<p><span class="autocomment">Övning 1.2:2</span></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 7 juni 2007 kl. 09.57</td>
</tr>
<tr><td colspan="2" align="left"><strong>Rad 164:</strong></td>
<td colspan="2" align="left"><strong>Rad 164:</strong></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos x^2 \cdot 2x$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\cos x^2 \cdot 2x$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">b)</td></td></tr>
<tr><td>-</td><td style="background: #ffa; font-size: smaller;"><td class="ntext" width="33%">$<span style="color: red; font-weight: bold;">\</span>e^{x^2+x}(2x+1)$</td></td><td>+</td><td style="background: #cfc; font-size: smaller;"><td class="ntext" width="33%">$e^{x^2+x}(2x+1)$</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">c)</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext">c)</td></td></tr>
<tr><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle - \frac{\sin x}{2\sqrt{\cos x}}$</td></td><td> </td><td style="background: #eee; font-size: smaller;"><td class="ntext" width="33%">$\displaystyle - \frac{\sin x}{2\sqrt{\cos x}}$</td></td></tr>
</table>
KTH.SE:u1zpa8nw