document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92310>Question 92310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the horizontal and vertical asymptotes of the following:\r<BR>\n" );
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document.write( "A) f(x)= 2x+3/x+2\r<BR>\n" );
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document.write( "B) g(x)= 5x / x^2+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67173 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=67173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) f(x)= (2x + 3)/(x + 2)<BR>\n" );
document.write( "Vertical Asymptote:<BR>\n" );
document.write( "x = -2 because of the denominator<BR>\n" );
document.write( "Horizontal Asymptope:<BR>\n" );
document.write( "y = 2 derived from graphing or:<BR>\n" );
document.write( "lim[x ~> +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inf ALIGN=MIDDLE  ALT=\"inf\"   DISABLED_style= \"max-width:90%; height:auto;\" >] (2x + 3)/(x + 2)<BR>\n" );
document.write( "lim[x ~> +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inf ALIGN=MIDDLE  ALT=\"inf\"   DISABLED_style= \"max-width:90%; height:auto;\" >] 2(x^0)/(x^0) H' Theory<BR>\n" );
document.write( "2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%282x+%2B+3%29%2F%28x+%2B+2%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%282x+%2B+3%29%2F%28x+%2B+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B) g(x)= 5x / (x^2 + 1)<BR>\n" );
document.write( "Vertical Asymptote:<BR>\n" );
document.write( "none because of the denominator<BR>\n" );
document.write( "Horizontal Asymptope:<BR>\n" );
document.write( "y = 0 derived from graphing or:<BR>\n" );
document.write( "lim[x ~> +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inf ALIGN=MIDDLE  ALT=\"inf\"   DISABLED_style= \"max-width:90%; height:auto;\" >] 5x / (x^2 + 1)<BR>\n" );
document.write( "lim[x ~> +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inf ALIGN=MIDDLE  ALT=\"inf\"   DISABLED_style= \"max-width:90%; height:auto;\" >] 5/(2x) H' Theory<BR>\n" );
document.write( "(5/2) * lim[x ~> +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inf ALIGN=MIDDLE  ALT=\"inf\"   DISABLED_style= \"max-width:90%; height:auto;\" >] 1/x<BR>\n" );
document.write( "(5/2)(0) = 0<BR>\n" );
document.write( "But: g(0) = 0 ... no asymptote<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C200%2C-20%2C20%2C-2.5%2C2.5%2C5x+%2F+%28x%5E2+%2B+1%29%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C200%2C-20%2C20%2C-2.5%2C2.5%2C5x+%2F+%28x%5E2+%2B+1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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