9.1

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#006666" TEXT="#080000"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Cálculo 21"><U><B>Cálculo de una variable</B></U></A><B> | </B><A HREF="id543.htm" TARGET="_top" TITLE="D.G. Zill"><U><B>D. G. Zill</B></U></A><B> |</B></div> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>Ejercicios 9.1</B></div> <div> <B>Sucesiones</B></div> <bR> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3926688482" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <div>  <A NAME="top"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Top</div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="953" BORDERCOLORLIGHT="#006666" BORDERCOLORDARK="#006666" FRAME="VOID" RULES="NONE" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=2 BGCOLOR=#006666 HEIGHT= 23 WIDTH="943"><div> <B>Apuntes</B></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 23 WIDTH="471"><div> <A HREF="#def__sucesión" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011866990000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Definición de sucesi</B></U></A><A HREF="#def__sucesión" TITLE="9.1"><U><B>ón</B></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#teorema_9_1_1" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011866990000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Teorema 9.1.1</B></U></A><B>  </B><FONT SIZE="4" COLOR="#0066CC" FACE="Georgia" ><B> Límite de una sucesión</B></FONT></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 27 WIDTH="471"><div> <A HREF="#definición_9_1_2" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011866990000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Sucesión convergente</B></U></A></div> </tD> <tD VALIGN=TOP WIDTH="471"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="27" ALIGN="bottom" WIDTH="471" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 27 WIDTH="943"><div> <A HREF="#teorema_9_1_2" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011866990000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Teorema 9.1.2</B></U></A><B>  </B><FONT SIZE="4" COLOR="#0066CC" FACE="Georgia" ><B> Propiedades del límite de una sucesión</B></FONT></div> </tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 41 WIDTH="943"><div> <A HREF="#teorema_9_1_3" TITLE="9.1"><U><IMG SRC="2f9eec210.gif" border=0 width="492" height="33" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 41 WIDTH="943"><div> <A HREF="#teorema_9_1_4" TITLE="9.1"><U><IMG SRC="2f9f08210.gif" border=0 width="520" height="33" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 23 ><NOBR><div> <A HREF="#sucesión_definida_recursivamente" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011866990000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Sucesión definida recursivamente</B></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#teorema_9_1_5" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011866990000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Teorema 9.1.5</B></U></A><B>  </B><FONT SIZE="4" COLOR="#0066CC" FACE="Georgia" ><B> Teorema de compresión</B></FONT></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 23 WIDTH="471"><div> <A HREF="#factorial" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011866990000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Definición de Factorial</B></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#teorema_9_1_6__" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011866990000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Teorema 9.1.6</B></U></A><B>  </B><FONT SIZE="4" COLOR="#0066CC" FACE="Georgia" ><B> Sucesión de valores absolutos</B></FONT></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#CCFFFF HEIGHT= 23 ><NOBR><div> <A HREF="#ejercicios_9_1" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011800000000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Enunciados de los problemas (enlaces)</B></U></A></div> </NOBR></tD> <tD VALIGN=TOP BGCOLOR=#CCFFCC><NOBR><div> <A HREF="#lista_9_1" TITLE="9.1"><U><B><IMG BORDER="0" SRC="Symb075c00b7011800000000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Lista de reproducción del Ejercicio 9.1</B></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 BGCOLOR=#006666 HEIGHT= 20 WIDTH="943"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="20" ALIGN="bottom" WIDTH="943" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <div>  <A NAME="def__sucesión"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Def. sucesión</div> <div> <FONT SIZE="4" COLOR="#009966" FACE="Georgia" ><B>Definición 9.1.1  </B></FONT><B> </B><B>Su</B><B>ce</B><B>sión</B></div> <div> Una <B>sucesión infinita</B> es una función cuyo dominio es el conjunto completo de enteros positivos.</div> <div>  <A NAME="definición_9_1_2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Definición 9.1.2</div> <div> <FONT SIZE="4" COLOR="#009966" FACE="Georgia" ><B>Definición 9.1.2  </B></FONT><B> Sucesión con</B><B>v</B><B>ergente</B></div> <div> <B><IMG SRC="2f36d14c0.gif" border=0 width="977" height="76" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="teorema_9_1_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Teorema 9.1.1</div> <div> <B>Teorema 9.1.1  </B><FONT SIZE="4" COLOR="#0066CC" FACE="Georgia" ><B> Límite de una sucesión</B></FONT></div> <div> <B><IMG SRC="2f6d29480.gif" border=0 width="809" height="72" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="2f92e4480.gif" border=0 width="996" height="72" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="teorema_9_1_2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Teorema 9.1.2</div> <div> <B>Teorema 9.1.2  </B><FONT SIZE="4" COLOR="#0066CC" FACE="Georgia" ><B> Propiedades del límite de una sucesión</B></FONT></div> <div> <B><IMG SRC="2f9828130.gif" border=0 width="808" height="275" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="teorema_9_1_3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Teorema 9.1.3</div> <div> <B><IMG SRC="2f9ad7210.gif" border=0 width="471" height="33" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="2f9d68400.gif" border=0 width="872" height="64" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="teorema_9_1_4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Teorema 9.1.4</div> <div> <B><IMG SRC="2fa0f1210.gif" border=0 width="497" height="33" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="2fa1dd3b0.gif" border=0 width="733" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="sucesión_definida_recursivamente"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Sucesión definida recursivamente</div> <div> <B>Sucesión definida recursivamente</B></div> <div> Una sucsesión puede definirse especificando el primer término junto con una regla para obtener los términos subsecuentes a partir de los térmios precedentes. En este caso se dice que la sucesión está defiida recursivamente. La regla de definición se denomina <B>fórmula de recursión</B>.</div> <div>  <A NAME="teorema_9_1_5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Teorema 9.1.5</div> <div> <B>Teorema 9.1.5  </B><FONT SIZE="4" COLOR="#0066CC" FACE="Georgia" ><B> Teorema de compresión</B></FONT></div> <div> <B><IMG SRC="2fa2c17b0.gif" border=0 width="961" height="123" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="factorial"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Factorial</div> <div> <B>Factorial</B></div> <div> Si <I>n</I> es un entero positivo, el símbolo <I>n</I>!, que se lee “<I>n</I> factorial”, es el producto de los primeros <I>n</I> enteros positivos:</div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="2fa3d0200.gif" border=0 width="208" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="teorema_9_1_6__"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Teorema 9.1.6  </div> <div> <B>Teorema 9.1.6  </B><FONT SIZE="4" COLOR="#0066CC" FACE="Georgia" ><B> Sucesión de valores absolutos</B></FONT></div> <div> <B><IMG SRC="2fa46b230.gif" border=0 width="619" height="35" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <DIV ALIGN="LEFT"></DIV> <div>  <A NAME="ejercicios_9_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Ejercicios 9.1</div> <div> <B>Enunciados y soluciones de los problemas de los Ejercicios 9.1</B></div> <bR> <div> <FONT SIZE="5" COLOR="#006600" FACE="Bell MT" ><B>S</B></FONT>olución en imagen <IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> y o video <IMG SRC="265418180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> de los problemas de los Ejercicios 9.1:</div> <bR> <div> <FONT SIZE="4" COLOR="#006666" FACE="Bell MT" ><B>E</B></FONT>n los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" ><B>1</B> </FONT>a<FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" > <B>10</B></FONT>, liste los primeros cuatro términos de la sucesión cuyo término general es <I>a</I><FONT SIZE="3" COLOR="#000000" FACE="Bell MT" ><I>n</I></FONT><I>.</I></div> <div> <I><IMG SRC="2d5680330.gif" border=0 width="128" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="#1" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       <IMG SRC="2d5984330.gif" border=0 width="132" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="https://youtu.be/m7Cv-xAN914" TARGET="_top" TITLE="https://youtu.be/m7Cv-xAN914"><U><IMG SRC="2c10181a0.jpg" border=0 width="24" height="26" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       <IMG SRC="2d5a803b0.gif" border=0 width="128" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="https://youtu.be/m7Cv-xAN914?t=3m36s" TARGET="_top" TITLE="https://youtu.be/m7Cv-xAN914?t=3m36s"><U><IMG SRC="2c10181a0.jpg" border=0 width="24" height="26" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       <IMG SRC="2d57973b0.gif" border=0 width="151" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="#4" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       <IMG SRC="2d5b681d0.gif" border=0 width="104" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="https://youtu.be/n5PJ5pWGF4U" TARGET="_top" TITLE="https://youtu.be/n5PJ5pWGF4U"><U><IMG SRC="2c10181a0.jpg" border=0 width="24" height="26" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       </I></div> <div> <I><IMG SRC="2d58711d0.gif" border=0 width="113" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="#6" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       <IMG SRC="2d5c671d0.gif" border=0 width="103" height="29" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="https://youtu.be/n5PJ5pWGF4U?t=2m56s" TARGET="_top" TITLE="https://youtu.be/n5PJ5pWGF4U?t=2m56s"><U><IMG SRC="2c10181a0.jpg" border=0 width="24" height="26" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       <IMG SRC="2d5d77200.gif" border=0 width="119" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="#8" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       <IMG SRC="2d5e7b430.gif" border=0 width="123" height="67" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="https://youtu.be/q070f6YxZY4" TARGET="_top" TITLE="https://youtu.be/q070f6YxZY4"><U><IMG SRC="2c10181a0.jpg" border=0 width="24" height="26" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><I>       <IMG SRC="2d5f95430.gif" border=0 width="149" height="67" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I><A HREF="#10" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> <FONT SIZE="4" COLOR="#006666" FACE="Bell MT" ><B>E</B></FONT>n los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" ><B>11</B> </FONT>a<FONT SIZE="4" COLOR="#CC0033" FACE="Bell MT" > <B>14</B></FONT>, emplee la definición 9.1.2 para demostrar que cada sucesión converge al número <I>L</I> dado.</div> <div> <IMG SRC="2d65953b0.gif" border=0 width="149" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#11" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="2d66a03b0.gif" border=0 width="160" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0">        <IMG SRC="2d67ad3b0.gif" border=0 width="173" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#13" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="2d68b73d0.gif" border=0 width="183" height="61" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#14" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="4" COLOR="#006666" FACE="Bell MT" ><B>E</B></FONT><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >n los problemas </FONT><B>15</B> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >a</FONT> <B>46</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >, determine si la sucesión dada converge. Si la sucesión converge, entonces encuentre su límite.</FONT></div> <div> <IMG SRC="2f6e783b0.gif" border=0 width="120" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#9_1_15" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f70673b0.gif" border=0 width="103" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#16" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="2f72783b0.gif" border=0 width="120" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#17" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="2f74793b0.gif" border=0 width="121" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=kktcxttZEA0&t=294s" TARGET="_top" TITLE="https://www.youtube.com/watch?v=kktcxttZ"><U><IMG SRC="2c10181a0.jpg" border=0 width="24" height="26" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f75783b0.gif" border=0 width="120" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#19" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="2f777b3b0.gif" border=0 width="123" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=TItcwculIug" TARGET="_top" TITLE="https://www.youtube.com/watch?v=TItcwcul"><U><IMG SRC="265418180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="2f78a02d0.gif" border=0 width="160" height="45" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#21" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f7a7d480.gif" border=0 width="125" height="72" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=PfPn0fRU3VE" TARGET="_top" TITLE="https://www.youtube.com/watch?v=PfPn0fRU"><U><IMG SRC="265418180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="2f7c773d0.gif" border=0 width="119" height="61" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#23" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f7d773b0.gif" border=0 width="119" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=5T5o5nn5F04" TARGET="_top" TITLE="https://www.youtube.com/watch?v=5T5o5nn5"><U><IMG SRC="265418180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="2f7e69200.gif" border=0 width="105" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=nWRvlNH26RU" TARGET="_top" TITLE="https://www.youtube.com/watch?v=nWRvlNH2"><U><IMG SRC="265418180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f806d230.gif" border=0 width="109" height="35" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#26" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f8281400.gif" border=0 width="129" height="64" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#27" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f837c3b0.gif" border=0 width="124" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=hUO1AB7KmkI" TARGET="_top" TITLE="https://www.youtube.com/watch?v=hUO1AB7K"><U><IMG SRC="265418180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f8477200.gif" border=0 width="119" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://www.youtube.com/watch?v=oMAgGM7HHVY" TARGET="_top" TITLE="https://www.youtube.com/watch?v=oMAgGM7H"><U><IMG SRC="265418180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="2f8677200.gif" border=0 width="119" height="32" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#30" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f88653b0.gif" border=0 width="101" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#31" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f9197430.gif" border=0 width="151" height="67" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#32" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="2f94853d0.gif" border=0 width="133" height="61" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#33" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2f96783d0.gif" border=0 width="120" height="61" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#34" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="2fb1783d0.gif" border=0 width="120" height="61" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#35" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2fb07d3d0.gif" border=0 width="125" height="61" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#36" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2fb599400.gif" border=0 width="153" height="64" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#37" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>          <IMG SRC="2fb78f480.gif" border=0 width="143" height="72" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#38" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="2fbc933d0.gif" border=0 width="147" height="61" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#39" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="2fbec33b0.gif" border=0 width="195" height="59" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#40" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>         <IMG SRC="2fc26d4b0.gif" border=0 width="109" height="75" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#41" TITLE="9.1"><U><IMG SRC="265318180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <DIV ALIGN="LEFT"></DIV> <div>  <A NAME="lista_9_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Lista 9.1</div> <div> <B>Lista de reproducción de los Ejercicios 9.1</B></div> <bR> <div> <B> <iframe width="853" height="480" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo2y-GvFBGXkjSfgvzRRpJ9I" frameborder="0" allowfullscreen></iframe>  </B></div> <div> <B> <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>1</B></div> <div> <B><IMG SRC="2d6064e40.gif" border=0 width="868" height="484" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B> <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>4</B></div> <div> <B><IMG SRC="2d617b2d0.gif" border=0 width="891" height="557" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B> <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>6</B></div> <div> <B><IMG SRC="2d6260d00.gif" border=0 width="608" height="464" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B> <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>8</B></div> <div> <B><IMG SRC="2d63575f0.gif" border=0 width="855" height="351" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B> <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>10</B></div> <div> <B><IMG SRC="2d64747f0.gif" border=0 width="884" height="639" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>11</div> <div> <B><IMG SRC="2d691fe90.gif" border=0 width="799" height="745" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>13</div> <div> <B><IMG SRC="2d6a5f1b0.gif" border=0 width="863" height="795" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B> <A NAME="14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>14</B></div> <div> <B><IMG SRC="2d6b77430.gif" border=0 width="631" height="835" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="9_1_15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9.1.15</div> <div> <IMG SRC="2f6fe4e00.gif" border=0 width="996" height="480" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="16"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>16</div> <div> <IMG SRC="2f71e4670.gif" border=0 width="996" height="615" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>17</div> <div> <IMG SRC="2f739ba50.gif" border=0 width="667" height="677" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="19"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>19</div> <div> <IMG SRC="2f76e4b30.gif" border=0 width="996" height="691" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="21"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>21</div> <div> <IMG SRC="2f79e4750.gif" border=0 width="996" height="373" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="23"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>23</div> <div> <IMG SRC="2f7b8f7d0.gif" border=0 width="655" height="381" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="26"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>26</div> <div> <IMG SRC="2f7fb8110.gif" border=0 width="952" height="529" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="27"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>27</div> <div> <IMG SRC="2f81dca30.gif" border=0 width="988" height="931" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="30"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>30</div> <div> <IMG SRC="2f8535100.gif" border=0 width="565" height="272" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="31"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>31</div> <div> <IMG SRC="2f87dcb00.gif" border=0 width="988" height="432" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="32"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>32</div> <div> <TABLE BORDER="0" CELLPADDING="0" CELLSPACING="1" WIDTH="1010" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="VOID" RULES="NONE" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 164 WIDTH="1008"><div> <IMG SRC="2f8a289d0.gif" border=0 width="552" height="157" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 523 ><NOBR><div> <IMG SRC="2f8eeffd0.gif" border=0 width="495" height="509" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><bR> <bR> <bR> <bR> <bR> <bR> <bR> <div> <IMG SRC="2f8fde840.gif" border=0 width="478" height="388" ALT="Imagen de Paintbrush" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <div> <IMG SRC="2f90c8df0.gif" border=0 width="968" height="479" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="33"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>33</div> <div> <IMG SRC="2f931ce70.gif" border=0 width="540" height="487" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="34"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>34</div> <div> <IMG SRC="2f9573bb0.gif" border=0 width="627" height="443" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="35"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>35</div> <div> <TABLE BORDER="0" CELLPADDING="0" CELLSPACING="1" WIDTH="1010" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="VOID" RULES="NONE" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 155 WIDTH="1008"><div> <IMG SRC="2fa90c940.gif" border=0 width="524" height="148" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 495 ><NOBR><div> <IMG SRC="2faaf4e80.gif" border=0 width="500" height="488" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><bR> <bR> <div> <IMG SRC="2fade9ba0.gif" border=0 width="489" height="442" ALT="Imagen de Paintbrush" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <div> <IMG SRC="2faed5800.gif" border=0 width="981" height="640" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="36"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>36</div> <div> <IMG SRC="2fafe5280.gif" border=0 width="997" height="1064" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> 37</div> <div> <IMG SRC="2fb2e4f70.gif" border=0 width="996" height="1271" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="37"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>37</div> <div> <IMG SRC="2fb3695c0.gif" border=0 width="873" height="1116" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="38"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>38</div> <div> <IMG SRC="2fb6f3b00.gif" border=0 width="755" height="432" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="2fb88a880.gif" border=0 width="906" height="392" ALT="Imagen de Paintbrush" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="2fb9df410.gif" border=0 width="991" height="577" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="2fba80950.gif" border=0 width="896" height="405" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </div> <div>  <A NAME="39"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>39</div> <div> <IMG SRC="2fbbadb80.gif" border=0 width="685" height="440" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="40"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>40</div> <div> <IMG SRC="2fbdb0040.gif" border=0 width="944" height="260" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="2fbf3b860.gif" border=0 width="571" height="390" ALT="Imagen de Paintbrush" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="2fc0fbb10.gif" border=0 width="507" height="177" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="41"><IMG BORDER="0" 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