https://matte5.mathonline.se/index.php?action=history&feed=atom&title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde 2026-06-30T02:52:08Z Versionshistorik för denna sida på wikin MediaWiki 1.23.1 https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=22297&oldid=prev 2015-05-16T21:41:59Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 16 maj 2015 kl. 21.41</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 3:</td> <td colspan="2" class="diff-lineno">Rad 3:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| style=&quot;border-bottom:1px solid #797979&quot; width=&quot;5px&quot; | &amp;nbsp;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| style=&quot;border-bottom:1px solid #797979&quot; width=&quot;5px&quot; | &amp;nbsp;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.2 Genomsnittlig förändringshastighet|&lt;-- Förra avsnitt]]}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.2 Genomsnittlig förändringshastighet|&lt;-- Förra avsnitt]]}}</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.3 Gränsvärde|<del class="diffchange diffchange-inline">Teori</del>]]}}</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.3 Gränsvärde|<ins class="diffchange diffchange-inline">Genomgång</ins>]]}}</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Selected tab|[[2.3 Övningar till Gränsvärde|Övningar]]}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Selected tab|[[2.3 Övningar till Gränsvärde|Övningar]]}}</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.4 Derivatans definition|Nästa avsnitt --&gt;]]}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.4 Derivatans definition|Nästa avsnitt --&gt;]]}}</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=22295&oldid=prev 2015-05-16T21:39:27Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 16 maj 2015 kl. 21.39</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 199:</td> <td colspan="2" class="diff-lineno">Rad 199:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Matte:Copyrights|Copyright]] © 2011-<del class="diffchange diffchange-inline">2014 Taifun Alishenas</del>. All Rights Reserved.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Matte:Copyrights|Copyright]] © 2011-<ins class="diffchange diffchange-inline">2015 Math Online Sweden AB</ins>. All Rights Reserved.</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=17081&oldid=prev 2014-11-07T15:37:15Z

<p>‎<span dir="auto"><span class="autocomment">Övning 3</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 7 november 2014 kl. 15.37</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 70:</td> <td colspan="2" class="diff-lineno">Rad 70:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>d) &amp;nbsp;&amp;nbsp; Hur borde resultatet från c) tolkas?</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>d) &amp;nbsp;&amp;nbsp; Hur borde resultatet från c) tolkas?</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 3a|2.3a Svar 3a|Lösning 3a|2.3a Lösning 3a|Svar <del class="diffchange diffchange-inline">5b</del>|2.3a Svar 3b|Lösning 3b|2.3a Lösning 3b|Svar 3c|2.3a Svar 3c|Lösning 3c|2.3a Lösning 3c|Lösning 3d|2.3a Lösning 3d}}</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 3a|2.3a Svar 3a|Lösning 3a|2.3a Lösning 3a|Svar <ins class="diffchange diffchange-inline">3b</ins>|2.3a Svar 3b|Lösning 3b|2.3a Lösning 3b|Svar 3c|2.3a Svar 3c|Lösning 3c|2.3a Lösning 3c|Lösning 3d|2.3a Lösning 3d}}</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Övning 4 ==</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Övning 4 ==</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=16898&oldid=prev 2014-11-03T13:18:02Z

<p>‎<span dir="auto"><span class="autocomment">Övning 11</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 3 november 2014 kl. 13.18</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 192:</td> <td colspan="2" class="diff-lineno">Rad 192:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Börja med att förlänga uttrycket i limes med konjugatet och fortsätt sedan att förenkla det.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Börja med att förlänga uttrycket i limes med konjugatet och fortsätt sedan att förenkla det.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;strong&gt;&lt;span style=&quot;color:red&quot;&gt;Konjugatet&lt;/span&gt;&lt;/strong&gt; till &lt;math&gt; a + \sqrt{b} &lt;/math&gt; är &lt;math&gt; a - \sqrt{b} &lt;/math&gt;.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;strong&gt;&lt;span style=&quot;color:red&quot;&gt;Konjugatet&lt;/span&gt;&lt;/strong&gt; till &lt;math&gt; <ins class="diffchange diffchange-inline">{\color{White} x} </ins>a + \sqrt{b<ins class="diffchange diffchange-inline">} {\color{White} x</ins>} &lt;/math&gt; är &lt;math&gt; <ins class="diffchange diffchange-inline">{\color{White} x} </ins>a - \sqrt{b<ins class="diffchange diffchange-inline">} {\color{White} x</ins>} &lt;/math&gt; <ins class="diffchange diffchange-inline">och omvänt</ins>.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 11|2.3a Svar 11a|Lösning 11|2.3a Lösning 11}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 11|2.3a Svar 11a|Lösning 11|2.3a Lösning 11}}</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=16897&oldid=prev 2014-11-03T13:15:55Z

<p>‎<span dir="auto"><span class="autocomment">Övning 11</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 3 november 2014 kl. 13.15</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 190:</td> <td colspan="2" class="diff-lineno">Rad 190:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::&lt;math&gt; \lim_{x \to \infty}\,\,(\,x \,-\, \sqrt{x^2\,-\,x}\,) &lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::&lt;math&gt; \lim_{x \to \infty}\,\,(\,x \,-\, \sqrt{x^2\,-\,x}\,) &lt;/math&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Börja med att förlänga uttrycket i limes med konjugatet och fortsätt sedan att förenkla det. &lt;strong&gt;&lt;span style=&quot;color:red&quot;&gt;Konjugatet&lt;/span&gt;&lt;/strong&gt; till &lt;math&gt; a + \sqrt{b} &lt;/math&gt; är &lt;math&gt; a - \sqrt{b} &lt;/math&gt;.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Börja med att förlänga uttrycket i limes med konjugatet och fortsätt sedan att förenkla det.</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;strong&gt;&lt;span style=&quot;color:red&quot;&gt;Konjugatet&lt;/span&gt;&lt;/strong&gt; till &lt;math&gt; a + \sqrt{b} &lt;/math&gt; är &lt;math&gt; a - \sqrt{b} &lt;/math&gt;.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 11|2.3a Svar 11a|Lösning 11|2.3a Lösning 11}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 11|2.3a Svar 11a|Lösning 11|2.3a Lösning 11}}</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=16896&oldid=prev 2014-11-03T13:15:26Z

<p>‎<span dir="auto"><span class="autocomment">Övning 11</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 3 november 2014 kl. 13.15</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 190:</td> <td colspan="2" class="diff-lineno">Rad 190:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::&lt;math&gt; \lim_{x \to \infty}\,\,(\,x \,-\, \sqrt{x^2\,-\,x}\,) &lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::&lt;math&gt; \lim_{x \to \infty}\,\,(\,x \,-\, \sqrt{x^2\,-\,x}\,) &lt;/math&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Börja med att förlänga uttrycket i limes med konjugatet och fortsätt sedan att förenkla det. Konjugatet till &lt;math&gt; a + \sqrt{b} &lt;/math&gt; är &lt;math&gt; a - \sqrt{b} &lt;/math&gt;.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Börja med att förlänga uttrycket i limes med konjugatet och fortsätt sedan att förenkla det. <ins class="diffchange diffchange-inline">&lt;strong&gt;&lt;span style=&quot;color:red&quot;&gt;</ins>Konjugatet<ins class="diffchange diffchange-inline">&lt;/span&gt;&lt;/strong&gt; </ins>till &lt;math&gt; a + \sqrt{b} &lt;/math&gt; är &lt;math&gt; a - \sqrt{b} &lt;/math&gt;.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 11|2.3a Svar 11a|Lösning 11|2.3a Lösning 11}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 11|2.3a Svar 11a|Lösning 11|2.3a Lösning 11}}</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=16894&oldid=prev 2014-11-03T13:05:07Z

<p>‎<span dir="auto"><span class="autocomment">Övning 2</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 3 november 2014 kl. 13.05</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 51:</td> <td colspan="2" class="diff-lineno">Rad 51:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>e) &lt;math&gt; \displaystyle {\color{White} x} \lim_{x \to \infty}\, {3\,x\,+\,4 \over x} &lt;/math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>e) &lt;math&gt; \displaystyle {\color{White} x} \lim_{x \to \infty}\, {3\,x\,+\,4 \over x} &lt;/math&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 2a|2.3a Svar 2a|Lösning 2a|2.3a Lösning 2a|Svar 2b|2.3a Svar 2b|Lösning 2b|2.3a Lösning 2b|Svar 2c|2.3a Svar <del class="diffchange diffchange-inline">1c</del>|Lösning 2c|2.3a Lösning 2c|Svar 2d|2.3a Svar 2d|Lösning 2d|2.3a Lösning 2d|Svar 2e|2.3a Svar 2e|Lösning 2e|2.3a Lösning 2e}}</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;{{#NAVCONTENT:Svar 2a|2.3a Svar 2a|Lösning 2a|2.3a Lösning 2a|Svar 2b|2.3a Svar 2b|Lösning 2b|2.3a Lösning 2b|Svar 2c|2.3a Svar <ins class="diffchange diffchange-inline">2c</ins>|Lösning 2c|2.3a Lösning 2c|Svar 2d|2.3a Svar 2d|Lösning 2d|2.3a Lösning 2d|Svar 2e|2.3a Svar 2e|Lösning 2e|2.3a Lösning 2e}}</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Övning 3 ==</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Övning 3 ==</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=15974&oldid=prev 2014-10-11T10:36:18Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 11 oktober 2014 kl. 10.36</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 5:</td> <td colspan="2" class="diff-lineno">Rad 5:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.3 Gränsvärde|Teori]]}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.3 Gränsvärde|Teori]]}}</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Selected tab|[[2.3 Övningar till Gränsvärde|Övningar]]}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{Selected tab|[[2.3 Övningar till Gränsvärde|Övningar]]}}</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.4 Derivatans definition<del class="diffchange diffchange-inline">: Från sekanten till tangenten</del>|Nästa avsnitt --&gt;]]}}</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Not selected tab|[[2.4 Derivatans definition|Nästa avsnitt --&gt;]]}}</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| style=&quot;border-bottom:1px solid #797979&quot;&#160; width=&quot;100%&quot;| &amp;nbsp;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>| style=&quot;border-bottom:1px solid #797979&quot;&#160; width=&quot;100%&quot;| &amp;nbsp;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=15481&oldid=prev 2014-09-30T12:07:52Z

<p>‎<span dir="auto"><span class="autocomment">Övning 10</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 30 september 2014 kl. 12.07</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 178:</td> <td colspan="2" class="diff-lineno">Rad 178:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Beräkna gränsvärdet</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Beräkna gränsvärdet</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::&lt;math&gt; \lim_{x \to 1}\,\,{x^3\,-\,1 \over x^2\,<del class="diffchange diffchange-inline">+</del>\,6\,x\,+\,5} &lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::&lt;math&gt; \lim_{x \to 1}\,\,{x^3\,-\,1 \over x^2\,<ins class="diffchange diffchange-inline">-</ins>\,6\,x\,+\,5} &lt;/math&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Faktorisera uttryckets täljare och nämnare och förkorta det.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Faktorisera uttryckets täljare och nämnare och förkorta det.</div></td></tr> </table>

Taifun https://matte5.mathonline.se/index.php?title=2.3_%C3%96vningar_till_Gr%C3%A4nsv%C3%A4rde&diff=15480&oldid=prev 2014-09-30T12:07:05Z

<p>‎<span dir="auto"><span class="autocomment">Övning 10</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 30 september 2014 kl. 12.07</td> </tr><tr><td colspan="2" class="diff-lineno">Rad 178:</td> <td colspan="2" class="diff-lineno">Rad 178:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Beräkna gränsvärdet</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Beräkna gränsvärdet</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::&lt;math&gt; \lim_{x \to 1}\,\,{x^3\,-\,1 \over x^2\,+\,<del class="diffchange diffchange-inline">2</del>\,x\,<del class="diffchange diffchange-inline">-</del>\,<del class="diffchange diffchange-inline">3</del>} &lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::&lt;math&gt; \lim_{x \to 1}\,\,{x^3\,-\,1 \over x^2\,+\,<ins class="diffchange diffchange-inline">6</ins>\,x\,<ins class="diffchange diffchange-inline">+</ins>\,<ins class="diffchange diffchange-inline">5</ins>} &lt;/math&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Faktorisera uttryckets täljare och nämnare och förkorta det.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;b&gt;Ledning:&lt;/b&gt; Faktorisera uttryckets täljare och nämnare och förkorta det.</div></td></tr> </table>

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