document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=989818>Question 989818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28lim%29x-%3E0 ALIGN=MIDDLE  ALT=\"%28lim%29x-%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x%5E2%29%2F%28x%5E2%2B9%29%29cos%282%2Fx%29+ ALIGN=MIDDLE  ALT=\"+%28%28x%5E2%29%2F%28x%5E2%2B9%29%29cos%282%2Fx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > exists. Please show the steps needed in order to solve.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #610046 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=610046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Move <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \cos\left(\frac{2}{x}\right)\"> into the numerator of the rational function factor.\r<BR>\n" );
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document.write( "Then use the fact that the limit of a quotient is the quotient of the limits of the numerator and denominator.  The denominator limit is trivial, but you will have to use the Squeeze Theorem for the numerator.\r<BR>\n" );
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document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -1\ \leq\ \cos\left(\frac{2}{x}\right)\ \leq\ 1\">  therefore <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -x^2\ \leq\ x^2\cos\left(\frac{2}{x}\right)\ \leq\ x^2\">\r<BR>\n" );
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document.write( "Hence your numerator limit is the meat on a sandwich made out of zero bread.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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