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Límites laterales - Historial de revisiones
2024-03-28T10:14:48Z
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http://www.wikillerato.org/index.php?title=L%C3%ADmites_laterales&diff=18112&oldid=prev
Fjmolina en 11:34 10 ago 2010
2010-08-10T11:34:27Z
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 11:34 10 ago 2010</td>
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<tr><td colspan="2" class="diff-lineno">Línea 1:</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Límite por la derecha==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Límite por la derecha==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 189:</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></center></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Se </del>tiene que</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">se </ins>tiene que</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
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Fjmolina
http://www.wikillerato.org/index.php?title=L%C3%ADmites_laterales&diff=18111&oldid=prev
Fjmolina en 11:33 10 ago 2010
2010-08-10T11:33:36Z
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 11:33 10 ago 2010</td>
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<tr><td colspan="2" class="diff-lineno">Línea 1:</td>
<td colspan="2" class="diff-lineno">Línea 1:</td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Límite por la derecha==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Límite por la derecha==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 20:</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>_{n \in N}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>_{n \in N}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; cuyos <del style="color: red; font-weight: bold; text-decoration: none;">términos </del>son todos mayores que &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; cuyos <ins style="color: red; font-weight: bold; text-decoration: none;">terminos </ins>son todos mayores que &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 68:</td>
<td colspan="2" class="diff-lineno">Línea 69:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; lo suficientemente <del style="color: red; font-weight: bold; text-decoration: none;">próximo </del>a &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; lo suficientemente <ins style="color: red; font-weight: bold; text-decoration: none;">proximo </ins>a &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 97:</td>
<td colspan="2" class="diff-lineno">Línea 98:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>_{n \in N}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>_{n \in N}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; cuyos <del style="color: red; font-weight: bold; text-decoration: none;">términos </del>son todos menores que &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; cuyos <ins style="color: red; font-weight: bold; text-decoration: none;">terminos </ins>son todos menores que &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 145:</td>
<td colspan="2" class="diff-lineno">Línea 146:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; lo suficientemente <del style="color: red; font-weight: bold; text-decoration: none;">próximo </del>a &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; lo suficientemente <ins style="color: red; font-weight: bold; text-decoration: none;">proximo </ins>a &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&nbsp; por la izquierda.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&nbsp; por la izquierda.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Ejemplo==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Consideremos la función</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\mathrm{f} \left( \, x \, \right) =</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left\{</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \begin{array}{ll}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> x^2 & , \quad \text{ si } x > 2</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \\</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> 2 \cdot x - 1 & , \quad \text{ si } 2 \ge x</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \end{array}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">y calculemos ambos limites laterales cuando </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">x </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">tiende a dos.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Como para valores de </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">x</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">mayores que dos </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\mathrm{f} \left( \, x \, \right) = x^2</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Se tiene que</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\lim_{x \to 2^+} \mathrm{f} \left( \, x \, \right) =</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\lim_{x \to 2^+} x^2 = 4</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Para calcular el otro limite lateral, tenemos en cuenta que</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">cuando</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">x</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">es menor que dos</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\mathrm{f} \left( \, x \, \right) = 2 \cdot x - 1</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">y, por lo tanto</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\lim_{x \to 2^-} \mathrm{f} \left( \, x \, \right) =</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\lim_{x \to 2^-}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, 2 \cdot x - 1 \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> = 3</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
</table>
Fjmolina
http://www.wikillerato.org/index.php?title=L%C3%ADmites_laterales&diff=15310&oldid=prev
84.122.179.83 en 00:53 30 nov 2009
2009-11-30T00:53:48Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 00:53 30 nov 2009</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Línea 20:</td>
<td colspan="2" class="diff-lineno">Línea 20:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>_{n \in N}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>_{n \in N}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; cuyos <del style="color: red; font-weight: bold; text-decoration: none;">terminos </del>son todos mayores que &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; cuyos <ins style="color: red; font-weight: bold; text-decoration: none;">términos </ins>son todos mayores que &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 68:</td>
<td colspan="2" class="diff-lineno">Línea 68:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; lo suficientemente <del style="color: red; font-weight: bold; text-decoration: none;">proximo </del>a &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; lo suficientemente <ins style="color: red; font-weight: bold; text-decoration: none;">próximo </ins>a &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 97:</td>
<td colspan="2" class="diff-lineno">Línea 97:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>_{n \in N}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>_{n \in N}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; cuyos <del style="color: red; font-weight: bold; text-decoration: none;">terminos </del>son todos menores que &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; cuyos <ins style="color: red; font-weight: bold; text-decoration: none;">términos </ins>son todos menores que &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 145:</td>
<td colspan="2" class="diff-lineno">Línea 145:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; lo suficientemente <del style="color: red; font-weight: bold; text-decoration: none;">proximo </del>a &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; lo suficientemente <ins style="color: red; font-weight: bold; text-decoration: none;">próximo </ins>a &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_0</div></td></tr>
</table>
84.122.179.83
http://www.wikillerato.org/index.php?title=L%C3%ADmites_laterales&diff=3048&oldid=prev
Fjmolina en 15:03 11 ene 2007
2007-01-11T15:03:38Z
<p></p>
<table style="background-color: white; color:black;">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr>
<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 15:03 11 ene 2007</td>
</tr>
<tr><td colspan="2" class="diff-lineno">Línea 1:</td>
<td colspan="2" class="diff-lineno">Línea 1:</td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Se dice que el límite por la derecha de una función &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Límite por la derecha==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Se dice que el <ins style="color: red; font-weight: bold; text-decoration: none;">'''''</ins>límite por la derecha<ins style="color: red; font-weight: bold; text-decoration: none;">''''' </ins>de una función &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f}</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 72:</td>
<td colspan="2" class="diff-lineno">Línea 76:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Se dice que el límite por la izquierda de una función &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Límite por la izquierda==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Se dice que el <ins style="color: red; font-weight: bold; text-decoration: none;">'''''</ins>límite por la izquierda<ins style="color: red; font-weight: bold; text-decoration: none;">''''' </ins>de una función &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f}</div></td></tr>
</table>
Fjmolina
http://www.wikillerato.org/index.php?title=L%C3%ADmites_laterales&diff=2999&oldid=prev
Fjmolina en 02:03 11 ene 2007
2007-01-11T02:03:02Z
<p></p>
<p><b>Página nueva</b></p><div>Se dice que el límite por la derecha de una función &nbsp;<br />
<math><br />
\mathrm{f}<br />
</math><br />
&nbsp; en el punto &nbsp;<br />
<math><br />
x_0<br />
</math><br />
&nbsp; es &nbsp;<br />
<math><br />
L<br />
</math><br />
, si toda sucesión &nbsp;<br />
<math><br />
\left( \, x_n \, \right)<br />
_{n \in N}<br />
</math><br />
&nbsp; cuyos terminos son todos mayores que &nbsp;<br />
<math><br />
x_0<br />
</math><br />
&nbsp; y que tiende a &nbsp;<br />
<math><br />
x_0<br />
</math><br />
&nbsp; verifica<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\lim_{n \to \infty} \mathrm{f} \left( \, x_n \, \right) \, = \, L<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
El límite por la derecha se denota por<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\lim_{x \to x_0^+} \mathrm{f} \left( \, x \, \right)<br />
</math><br />
&nbsp; &nbsp; &nbsp; o bien &nbsp; &nbsp; &nbsp;<br />
<math><br />
\lim_{{ x \to x_0 \atop x > x_0}} \mathrm{f} \left( \, x \, \right)<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
El que la anterior igualdad sea cierta significa que podemos hacer &nbsp;<br />
<math><br />
\mathrm{f} \left( \, x \, \right)<br />
</math><br />
&nbsp; tan cercano a &nbsp;<br />
<math><br />
L<br />
</math><br />
&nbsp; como queramos eligiendo &nbsp;<br />
<math><br />
x<br />
</math><br />
&nbsp; lo suficientemente proximo a &nbsp;<br />
<math><br />
x_0<br />
</math><br />
&nbsp; por la derecha.<br />
<br />
<br/><br />
<br />
Se dice que el límite por la izquierda de una función &nbsp;<br />
<math><br />
\mathrm{f}<br />
</math><br />
&nbsp; en el punto &nbsp;<br />
<math><br />
x_0<br />
</math><br />
&nbsp; es &nbsp;<br />
<math><br />
L<br />
</math><br />
, si toda sucesión &nbsp;<br />
<math><br />
\left( \, x_n \, \right)<br />
_{n \in N}<br />
</math><br />
&nbsp; cuyos terminos son todos menores que &nbsp;<br />
<math><br />
x_0<br />
</math><br />
&nbsp; y que tiende a &nbsp;<br />
<math><br />
x_0<br />
</math><br />
&nbsp; verifica<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\lim_{n \to \infty} \mathrm{f} \left( \, x_n \, \right) \, = \, L<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
El límite por la izquierda se denota por<br />
<br />
<br/><br />
<br />
<center><br />
<math><br />
\lim_{x \to x_0^-} \mathrm{f} \left( \, x \, \right)<br />
</math><br />
&nbsp; &nbsp; &nbsp; o bien &nbsp; &nbsp; &nbsp;<br />
<math><br />
\lim_{{ x \to x_0 \atop x_0 > x}} \mathrm{f} \left( \, x \, \right)<br />
</math><br />
</center><br />
<br />
<br/><br />
<br />
El que la anterior igualdad sea cierta significa que podemos hacer &nbsp;<br />
<math><br />
\mathrm{f} \left( \, x \, \right)<br />
</math><br />
&nbsp; tan cercano a &nbsp;<br />
<math><br />
L<br />
</math><br />
&nbsp; como queramos eligiendo &nbsp;<br />
<math><br />
x<br />
</math><br />
&nbsp; lo suficientemente proximo a &nbsp;<br />
<math><br />
x_0<br />
</math><br />
&nbsp; por la izquierda.<br />
<br />
<br/><br />
<br />
[[Category:Matemáticas]]</div>
Fjmolina