Miscelánea2

<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><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> <A HREF="id417.htm" TARGET="_top" TITLE="Miscelánea1"><U>Miscelánea1</U></A>   |   <B>Miscelánea2</B>   |   <A HREF="id486.htm" TARGET="_top" TITLE="Miscelánea3"><U>Miscelánea3</U></A></div> <div> </div> </td> </tr><tr> <td valign="top" width=77 BGCOLOR="#009999" TEXT="#080000"> <bR> <bR> <bR> <div> <A HREF="id465_m.htm#enunciados" TARGET="TRLX_Middle" TITLE="Miscelánea2"><U><B> <img src="HTMLobj-5716/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> <B> <A NAME="enunciados"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>Miscelánea2</B></div> <div> <B> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="612" BORDERCOLORLIGHT="#33FFCC" BORDERCOLORDARK="#339900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 48 WIDTH="198"><div> <A HREF="#1" TITLE="Miscelánea2"><U><IMG SRC="165070290.gif" border=0 width="112" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#2" TITLE="Miscelánea2"><U><IMG SRC="165297290.gif" border=0 width="151" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#3" TITLE="Miscelánea2"><U><IMG SRC="165667290.gif" border=0 width="103" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 52 WIDTH="198"><div> <A HREF="#4" TITLE="Miscelánea2"><U><IMG SRC="16595d290.gif" border=0 width="93" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#5" TITLE="Miscelánea2"><U><IMG SRC="165d7c2d0.gif" border=0 width="124" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#6" TITLE="Miscelánea2"><U><IMG SRC="165f742b0.gif" border=0 width="116" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 48 WIDTH="198"><div> <A HREF="#7" TITLE="Miscelánea2"><U><IMG SRC="166379290.gif" border=0 width="121" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#8" TITLE="Miscelánea2"><U><IMG SRC="16656f290.gif" border=0 width="111" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#9" TITLE="Miscelánea2"><U><IMG SRC="166b601f0.gif" border=0 width="96" height="31" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 50 WIDTH="198"><div> <A HREF="#10" TITLE="Miscelánea2"><U><IMG SRC="16766f2b0.gif" border=0 width="111" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#11" TITLE="Miscelánea2"><U><IMG SRC="191a67270.gif" border=0 width="103" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#12" TITLE="Miscelánea2"><U><IMG SRC="191d8b270.gif" border=0 width="139" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 50 WIDTH="198"><div> <A HREF="#13" TITLE="Miscelánea2"><U><IMG SRC="19216d2b0.gif" border=0 width="109" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP><NOBR><div> <A HREF="#14" TITLE="Miscelánea2"><U><IMG SRC="192491280.gif" border=0 width="145" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#15" TITLE="Miscelánea2"><U><IMG SRC="192770270.gif" border=0 width="112" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 46 WIDTH="198"><div> <A HREF="#16" TITLE="Miscelánea2"><U><IMG SRC="192a70270.gif" border=0 width="112" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="46" ALIGN="bottom" WIDTH="198" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="198"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="46" ALIGN="bottom" WIDTH="198" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></B></div> <div> <B>S o l u c i o n e s</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><IMG SRC="164f70290.gif" border=0 width="112" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="16513fad0.gif" border=0 width="575" height="173" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B> <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="165397290.gif" border=0 width="151" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="165567850.gif" border=0 width="615" height="133" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="165767290.gif" border=0 width="103" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="165885f40.gif" border=0 width="389" height="244" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="165a5d290.gif" border=0 width="93" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="165b00cd0.gif" border=0 width="512" height="205" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" 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="165c7c2d0.gif" border=0 width="124" height="45" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="165e5c0b0.gif" border=0 width="604" height="267" 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="1660742b0.gif" border=0 width="116" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="1661e01b0.gif" border=0 width="480" height="283" 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="166279290.gif" border=0 width="121" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="1664e8700.gif" border=0 width="488" height="112" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="16666f290.gif" border=0 width="111" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="16672f430.gif" border=0 width="303" height="67" 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="166c601f0.gif" border=0 width="96" height="31" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="166d235f0.gif" border=0 width="547" height="95" 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="16776f2b0.gif" border=0 width="111" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="1678686d0.gif" border=0 width="616" height="109" 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="191b67270.gif" border=0 width="103" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="191c2dc50.gif" border=0 width="557" height="197" 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="191e8b270.gif" border=0 width="139" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="191ffdc40.gif" border=0 width="509" height="196" 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="19206d2b0.gif" border=0 width="109" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="192259d70.gif" border=0 width="601" height="215" 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="192391280.gif" border=0 width="145" height="40" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="192660db0.gif" border=0 width="608" height="219" 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="192870270.gif" border=0 width="112" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="1929d12d0.gif" border=0 width="465" height="301" 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="192b70270.gif" border=0 width="112" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="192d64680.gif" border=0 width="612" height="360" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <bR> <bR> <bR> <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"> <bR> </td> </tr></table></body>