document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=361546>Question 361546</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve this equation: Evaluate the following limits or explain why they do not exist. <BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+lim%28x-%3E0%2C+%28xcosx-sinx%29%2Fx+%29+ ALIGN=MIDDLE  ALT=\"+lim%28x-%3E0%2C+%28xcosx-sinx%29%2Fx+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+lim%28x-%3Einfinity%2C+%28e%5Ex-2%5Ex%29%2Fx+%29+ ALIGN=MIDDLE  ALT=\"+lim%28x-%3Einfinity%2C+%28e%5Ex-2%5Ex%29%2Fx+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+lim%28x-%3E1%2C++%28x%2F%28x-1%29+-+%281%2Flnx%29+%29+%29+ ALIGN=MIDDLE  ALT=\"+lim%28x-%3E1%2C++%28x%2F%28x-1%29+-+%281%2Flnx%29+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257769 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=257769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\rightarrow 0}\ \frac{x\cos(x)\ -\ \sin(x)}{x}\">\r<BR>\n" );
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document.write( "This is the indeterminate form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{0}{0}\">\r<BR>\n" );
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document.write( "so apply L'Hôpital's Rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\rightarrow c}\ \frac{f(x)}{g(x)}\ =\ \lim_{x\rightarrow c}\ \frac{f'(x)}{g'(x)}\">\r<BR>\n" );
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document.write( "Using the Product and Sum rules on the numerator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\rightarrow 0}\ \frac{cos(x)\ -\ x\sin(x)\ -\ \cos(x)}{1}\ =\ \lim_{x\rightarrow 0}\ \frac{x\sin(x)}{1}\ =\ 0\">\r<BR>\n" );
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document.write( "b.  Works the same way.\r<BR>\n" );
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document.write( "c.  You need to combine the two fractions so that you will have a <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{0}{0}\"> indeterminate form.\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<BR>\n" );
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