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2.3a Lösning 6d - Versionshistorik
2026-06-20T08:31:02Z
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Taifun den 28 september 2014 kl. 16.17
2014-09-28T16:17:02Z
<p></p>
<table class='diff diff-contentalign-left'>
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<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 28 september 2014 kl. 16.17</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1/x\,+\,1/x^2 \over 1\,+\,1/x^2} \,=\, {0\,+\,0 \over 1\,+\,0} <del class="diffchange diffchange-inline"> </del>\,=\, 0 </math></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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1/x\,+\,1/x^2 \over 1\,+\,1/x^2} \,=\, {0\,+\,0 \over 1\,+\,0} <ins class="diffchange diffchange-inline">\,=\, {0 \over 1} </ins>\,=\, 0 </math></div></td></tr>
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Taifun
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Taifun den 28 september 2014 kl. 16.15
2014-09-28T16:15:50Z
<p></p>
<table class='diff diff-contentalign-left'>
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<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 28 september 2014 kl. 16.15</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1/x\,+\,1/x^2 \over 1\,+\,1/x^2}  </math></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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1/x\,+\,1/x^2 \over 1\,+\,1/x^2<ins class="diffchange diffchange-inline">} \,=\, {0\,+\,0 \over 1\,+\,0</ins>}  <ins class="diffchange diffchange-inline">\,=\, 0 </ins></math></div></td></tr>
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Taifun
https://minidemo.mathonline.se/index.php?title=2.3a_L%C3%B6sning_6d&diff=15319&oldid=prev
Taifun den 28 september 2014 kl. 16.14
2014-09-28T16:14:13Z
<p></p>
<table class='diff diff-contentalign-left'>
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<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 28 september 2014 kl. 16.14</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1/x\,+\,1/x^2 \over <del class="diffchange diffchange-inline">2</del>\,+\,<del class="diffchange diffchange-inline">5/x\,-\,3</del>/x^2}  </math></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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1/x\,+\,1/x^2 \over <ins class="diffchange diffchange-inline">1</ins>\,+\,<ins class="diffchange diffchange-inline">1</ins>/x^2}  </math></div></td></tr>
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Taifun
https://minidemo.mathonline.se/index.php?title=2.3a_L%C3%B6sning_6d&diff=15318&oldid=prev
Taifun den 28 september 2014 kl. 16.13
2014-09-28T16:13:42Z
<p></p>
<table class='diff diff-contentalign-left'>
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<col class='diff-marker' />
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<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 28 september 2014 kl. 16.13</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1<del class="diffchange diffchange-inline">\,-\,2</del>/x\,+\,<del class="diffchange diffchange-inline">3</del>/x^2 \over 2\,+\,5/x\,-\,3/x^2}  </math></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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1/x\,+\,<ins class="diffchange diffchange-inline">1</ins>/x^2 \over 2\,+\,5/x\,-\,3/x^2}  </math></div></td></tr>
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Taifun
https://minidemo.mathonline.se/index.php?title=2.3a_L%C3%B6sning_6d&diff=15317&oldid=prev
Taifun den 28 september 2014 kl. 16.13
2014-09-28T16:13:03Z
<p></p>
<table class='diff diff-contentalign-left'>
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<col class='diff-marker' />
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<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 28 september 2014 kl. 16.13</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over <del class="diffchange diffchange-inline">2\,</del>x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1\,-\,2/x\,+\,3/x^2 \over 2\,+\,5/x\,-\,3/x^2}  </math></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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} \, = \, \lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1\,-\,2/x\,+\,3/x^2 \over 2\,+\,5/x\,-\,3/x^2}  </math></div></td></tr>
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Taifun
https://minidemo.mathonline.se/index.php?title=2.3a_L%C3%B6sning_6d&diff=15316&oldid=prev
Taifun den 28 september 2014 kl. 16.12
2014-09-28T16:12:35Z
<p></p>
<table class='diff diff-contentalign-left'>
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<col class='diff-marker' />
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<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 28 september 2014 kl. 16.12</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} <del class="diffchange diffchange-inline">& </del>= <del class="diffchange diffchange-inline">& </del>\lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over 2\,x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1\,-\,2/x\,+\,3/x^2 \over 2\,+\,5/x\,-\,3/x^2}  </math></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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} <ins class="diffchange diffchange-inline">\, </ins>= <ins class="diffchange diffchange-inline">\, </ins>\lim_{x \to \infty}\,\, {x/x^2\,+\,1/x^2 \over 2\,x^2/x^2\,+\,1/x^2} \,=\, \lim_{x \to \infty}\,\, {1\,-\,2/x\,+\,3/x^2 \over 2\,+\,5/x\,-\,3/x^2}  </math></div></td></tr>
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Taifun
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Taifun den 28 september 2014 kl. 16.12
2014-09-28T16:12:04Z
<p></p>
<table class='diff diff-contentalign-left'>
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<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 28 september 2014 kl. 16.12</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</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>:<math> <del class="diffchange diffchange-inline">\begin{array}{rcl} </del>\lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} & = & \lim_{x \to \infty}\,\, {<del class="diffchange diffchange-inline">x^2/x^2\,-\,2\,</del>x/x^2\,+\,<del class="diffchange diffchange-inline">3</del>/x^2 \over 2\,x^2/x^2\,+\,<del class="diffchange diffchange-inline">5\,x/x^2\,-\,3</del>/x^2} \,=\, \lim_{x \to \infty}\,\, {1\,-\,2/x\,+\,3/x^2 \over 2\,+\,5/x\,-\,3/x^2}  <del class="diffchange diffchange-inline">\\</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>:<math> \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} & = & \lim_{x \to \infty}\,\, {x/x^2\,+\,<ins class="diffchange diffchange-inline">1</ins>/x^2 \over 2\,x^2/x^2\,+\,<ins class="diffchange diffchange-inline">1</ins>/x^2} \,=\, \lim_{x \to \infty}\,\, {1\,-\,2/x\,+\,3/x^2 \over 2\,+\,5/x\,-\,3/x^2}  </math></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><del class="diffchange diffchange-inline">                                                                                                                        \\</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></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><del class="diffchange diffchange-inline">                                                                                                    & = & {1\,-\,0\,+\,0 \over 2\,+\,0\,-\,0} \,=\, {1 \over 2} \end{array}</del></math></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></div></td></tr>
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Taifun
https://minidemo.mathonline.se/index.php?title=2.3a_L%C3%B6sning_6d&diff=15314&oldid=prev
Taifun: Skapade sidan med ':<math> \begin{array}{rcl} \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} & = & \lim_{x \to \infty}\,\, {x^2/x^2\,-\,2\,x/x^2\,+\,3/x^2 \over 2\,x^2/x^2\,+\,5\,x/x^2\,-\,3/...'
2014-09-28T16:09:59Z
<p>Skapade sidan med ':<math> \begin{array}{rcl} \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} & = & \lim_{x \to \infty}\,\, {x^2/x^2\,-\,2\,x/x^2\,+\,3/x^2 \over 2\,x^2/x^2\,+\,5\,x/x^2\,-\,3/...'</p>
<p><b>Ny sida</b></p><div>:<math> \begin{array}{rcl} \lim_{x \to \infty}\,\, {x\,+\,1 \over x^2\,+\,1} & = & \lim_{x \to \infty}\,\, {x^2/x^2\,-\,2\,x/x^2\,+\,3/x^2 \over 2\,x^2/x^2\,+\,5\,x/x^2\,-\,3/x^2} \,=\, \lim_{x \to \infty}\,\, {1\,-\,2/x\,+\,3/x^2 \over 2\,+\,5/x\,-\,3/x^2} \\<br />
\\<br />
& = & {1\,-\,0\,+\,0 \over 2\,+\,0\,-\,0} \,=\, {1 \over 2} \end{array}</math></div>
Taifun