Miscelánea1

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=77 BGCOLOR="#009999" TEXT="#080000"> <div> <FONT SIZE="5" COLOR="#33FFCC" FACE="Arial" ><B>C á l c u l o  2 1</B></FONT><B>     </B><B>|     </B><A HREF="index.htm" TARGET="_top" TITLE="C á l c u l o 2 1"><U><B>Página principal</B></U></A><B>  |  </B><A HREF="id17.htm" TARGET="_top" TITLE="Contenido"><U><B>Contenido</B></U></A><B>  | </B><A HREF="id20.htm" TARGET="_top" TITLE="Límites y continuidad"><U><B>Límites y continuidad </B></U></A><B> | </B><A HREF="id463.htm" TARGET="_top" TITLE="Miscelánea de ejercicios de límites"><U><B>Misceláneas</B></U></A><B> |</B></div> <div> <B>Miscelánea1</B><B>   |   </B><A HREF="id465.htm" TARGET="_top" TITLE="Miscelánea2"><U>Miscelánea2</U></A><B>   |   </B><A HREF="id486.htm" TARGET="_top" TITLE="Miscelánea3"><U>Miscelánea3</U></A></div> <div> </div> </td> </tr><tr> <td valign="top" width=63 BGCOLOR="#009999" TEXT="#080000"> <bR> <bR> <div> <A HREF="id417_m.htm#enunciados_de_los_ejercicios" TARGET="TRLX_Middle" TITLE="Miscelánea1"><U><B> <img src="HTMLobj-2366/aniGif.gif" alt="Enunciados" border="0" align="bottom" width="50" height="50">  </B></U></A></div> </td> <td valign="top" height=382 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <FONT SIZE="4" COLOR="#0099FF" FACE="Times New Roman" ><B> <A NAME="enunciados_de_los_ejercicios"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B></FONT><B>Miscelánea1</B></div> <div> <B> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="634" BORDERCOLORLIGHT="#33FFCC" BORDERCOLORDARK="#339900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 51 ><NOBR><div> <A HREF="#1" TITLE="Miscelánea1"><U><IMG SRC="9317c2c0.gif" border=0 width="124" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="148"><div> <A HREF="#2" TITLE="Miscelánea1"><U><IMG SRC="9335b290.gif" border=0 width="91" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="159"><div> <A HREF="#3" TITLE="Miscelánea1"><U><IMG SRC="935582c0.gif" border=0 width="88" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#4" TITLE="Miscelánea1"><U><IMG SRC="93c8f290.gif" border=0 width="143" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 54 ><NOBR><div> <A HREF="#5" TITLE="Miscelánea1"><U><IMG SRC="a997f2f0.gif" border=0 width="127" height="47" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#6" TITLE="Miscelánea1"><U><IMG SRC="beb792c0.gif" border=0 width="121" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#7" TITLE="Miscelánea1"><U><IMG SRC="bee972c0.gif" border=0 width="151" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="156"><div> <A HREF="#8" TITLE="Miscelánea1"><U><IMG SRC="e6b612f0.gif" border=0 width="97" height="47" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 71 ><NOBR><div> <A HREF="#9" TITLE="Miscelánea1"><U><IMG SRC="1110782d0.gif" border=0 width="120" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#10" TITLE="Miscelánea1"><U><IMG SRC="119390300.gif" border=0 width="144" height="48" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#11" TITLE="Miscelánea1"><U><IMG SRC="119797400.gif" border=0 width="151" height="64" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#12" TITLE="Miscelánea1"><U><IMG SRC="119c85330.gif" border=0 width="133" height="51" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 52 ><NOBR><div> <A HREF="#13" TITLE="Miscelánea1"><U><IMG SRC="1207891d0.gif" border=0 width="137" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#14" TITLE="Miscelánea1"><U><IMG SRC="13d7802d0.gif" border=0 width="128" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#15" TITLE="Miscelánea1"><U><IMG SRC="13da9f2d0.gif" border=0 width="159" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#16" TITLE="Miscelánea1"><U><IMG SRC="14d6892c0.gif" border=0 width="137" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 62 ><NOBR><div> <A HREF="#17" TITLE="Miscelánea1"><U><IMG SRC="14da851d0.gif" border=0 width="133" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=2 WIDTH="310"><div> <A HREF="#18" TITLE="Miscelánea1"><U><IMG SRC="14df93370.gif" border=0 width="147" height="55" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#19" TITLE="Miscelánea1"><U><IMG SRC="16b299290.gif" border=0 width="153" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> </TABLE></B></div> <div> <B>S o l u c 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VSPACE="0"></div> <bR> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="a9a7f2f0.gif" border=0 width="127" height="47" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="a9b2c070.gif" border=0 width="556" height="263" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="bec792c0.gif" border=0 width="121" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="bed13d40.gif" border=0 width="531" height="212" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="bef972c0.gif" border=0 width="151" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="bf04c4b0.gif" border=0 width="588" height="331" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="e6c612f0.gif" border=0 width="97" height="47" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="e6e2c080.gif" border=0 width="300" height="264" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="110f782d0.gif" border=0 width="120" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="111158200.gif" border=0 width="600" height="288" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="119490300.gif" border=0 width="144" height="48" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <IMG SRC="11958fad0.gif" border=0 width="655" height="173" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="119697400.gif" border=0 width="151" height="64" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="119ba0bb0.gif" border=0 width="672" height="699" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="119d85330.gif" border=0 width="133" height="51" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="119fa5e30.gif" border=0 width="677" height="483" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="1208891d0.gif" border=0 width="137" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="12098c040.gif" border=0 width="652" height="260" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="13d8802d0.gif" border=0 width="128" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="13d928830.gif" border=0 width="552" height="387" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="13db9f2d0.gif" border=0 width="159" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="13dc1fcb0.gif" border=0 width="543" height="459" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="16"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="14d7892c0.gif" border=0 width="137" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="14d95c9b0.gif" border=0 width="604" height="155" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="14db851d0.gif" border=0 width="133" height="29" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="14dd2b350.gif" border=0 width="555" height="53" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="14de98370.gif" border=0 width="152" height="55" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="14e038200.gif" border=0 width="568" height="800" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="19"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="16b399290.gif" border=0 width="153" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="16b41d1d0.gif" border=0 width="541" height="285" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <bR> <bR> </td> <td valign="top" width=14 BGCOLOR="#009999" TEXT="#080000"> <bR> </td> </tr><tr> <td valign="top" colspan=3 height=21 BGCOLOR="#009999" TEXT="#080000"> <div> Si necesitas ayuda para comprender este tema escríbeme a <A HREF="mailto:calculo21@gmail.com" TARGET="_top" TITLE="mailto:calculo21@gmail.com"><U>Juan Beltrán</U></A> o a <A HREF="mailto:calculo21@hotmail.com" TARGET="_top" TITLE="mailto:calculo21@hotmail.com"><U>Cálculo21</U></A></div> </td> </tr></table></body>