Límites en el infinito

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=98 BGCOLOR="#006600" TEXT="#F7F7FF" bgproperties="fixed" background="05700732dwnpjk.jpg"> <div> <FONT SIZE="6" COLOR="#FFFFFF" FACE="Times New Roman" ><B>C á l c u l o   2 1</B></FONT><FONT SIZE="6" COLOR="#FFCC66" FACE="Arial" ><B> </B></FONT><FONT SIZE="2" COLOR="#FFFFCC" FACE="Arial" >   </FONT><B>  |   </B><A HREF="index.htm" TARGET="_top" TITLE="A n á l i s i s M a t e m á t i c o"><U><B>Home</B></U></A><B> |  </B><A HREF="id98.htm" TARGET="_top" TITLE=" | Contenido |"><U><B>Contenido</B></U></A><B> |  </B><A HREF="id293.htm" TARGET="_top" TITLE="Límites y continuidad"><U><B>Límites y continuidad</B></U></A><B> | </B></div> <div> <A HREF="id301.htm" TARGET="_top" TITLE="Teoremas de límites"><U>Teoremas de límites</U></A>   |   <A HREF="id295.htm" TARGET="_top" TITLE="Teorema de estricción"><U>Teorema de estricción</U></A>   |   <A HREF="id296.htm" TARGET="_top" TITLE="Límites unilaterales"><U>Límites unilaterales</U></A>   |   <A HREF="id297.htm" TARGET="_top" TITLE="Límites infinitos"><U>Límites infinitos</U></A>   |   Límites en el infinito   |   <A HREF="id299.htm" TARGET="_top" TITLE="Funciones continuas"><U>Funciones continuas</U></A>   |   <A HREF="id300.htm" TARGET="_top" TITLE="Misceláneas de ejercicios de límites"><U>Misceláneas de ejercicios de límites</U></A></div> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=56 BGCOLOR="#006600" TEXT="#F7F7FF"> <bR> </td> <td valign="top" height=361 colspan=2 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <U>Límites en el infinito</U></div> <div>  <A NAME="teorema_de_l_mite15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>Teorema de límite18:</B></FONT></div> <div> <IMG SRC="110de46b0.gif" border=0 width="484" height="107" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="as_ntota_horizontal"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#FF9999" FACE="Times New Roman" ><B>Asíntota horizontal:</B></FONT></div> <div> Una asíntota horizontal es una recta paralela al eje <I>x.</I></div> <div> <I><IMG SRC="110e15650.gif" border=0 width="533" height="101" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></I></div> <bR> <div>  <A NAME="teorema_de_l_mite19"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>Teorema de límite19:</B></FONT></div> <div> <B><IMG SRC="110fe5310.gif" border=0 width="229" height="49" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="559" BORDERCOLORLIGHT="#006600" BORDERCOLORDARK="#009900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=2 BGCOLOR=#FFFFCC HEIGHT= 39 WIDTH="549"><div>  <A NAME="ejercicios_resueltos"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0000" FACE="Times New Roman" ><B>Ejercicios resueltos</B></FONT></div> <bR> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 58 ><NOBR><div> <A HREF="#1" TITLE="Límites en el infinito"><U><IMG SRC="1110b9210.gif" border=0 width="185" height="33" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="273"><div> <A HREF="#2" TITLE="Límites en el infinito"><U><IMG SRC="1111ab330.gif" border=0 width="171" height="51" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 50 WIDTH="273"><div> <A HREF="#3" TITLE="Límites en el infinito"><U><IMG SRC="1112b02b0.gif" border=0 width="176" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="273"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="50" ALIGN="bottom" WIDTH="273" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <bR> <div> <B>S o l u c i o n e s</B></div> <bR> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0000" FACE="Times New Roman" ><B><IMG SRC="1113b9210.gif" border=0 width="185" height="33" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <div> <B><IMG SRC="1114cf530.gif" border=0 width="719" height="595" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0000" FACE="Times New Roman" ><IMG SRC="1115ab330.gif" border=0 width="171" height="51" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT></div> <div> <IMG SRC="1116b15b0.gif" border=0 width="689" height="347" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><IMG SRC="1117b02b0.gif" border=0 width="176" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="111874bf0.gif" border=0 width="628" height="191" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <bR> <bR> <bR> <bR> <bR> <bR> <bR> </td> </tr><tr> <td valign="top" colspan=2 height=21 BGCOLOR="#006600" TEXT="#F7F7FF"> <div> <B>| </B><A HREF="id298_m.htm#teorema_de_l_mite15" TARGET="TRLX_Middle" TITLE="Límites en el infinito"><U><B>Teorema de límite 18</B></U></A><B> | </B><A HREF="id298_m.htm#as_ntota_horizontal" TARGET="TRLX_Middle" TITLE="Límites en el infinito"><U><B>Asíntota horizontal</B></U></A><B> | </B><A HREF="id298_m.htm#teorema_de_l_mite19" TARGET="TRLX_Middle" TITLE="Límites en el infinito"><U><B>Teorema de límite 19</B></U></A><B> |</B><A HREF="id298_m.htm#ejercicios_resueltos" TARGET="TRLX_Middle" TITLE="Límites en el infinito"><U><B>Ejercicios resueltos</B></U></A></div> </td> </tr></table></body>