document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984535>Question 984535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have two limit questions:<BR>\n" );
document.write( "Find the derivative of f(x) = 2/x at x = -2.\r<BR>\n" );
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document.write( "Find the derivative of f(x) = -9/x  at x = -8. \r<BR>\n" );
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document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605310 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=605310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first problem to get you started.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x) = \frac{2}{x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x+h) = \frac{2}{x+h}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2}{x+h}-\frac{2}{x}}{h}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2x}{x(x+h)}-\frac{2}{x}}{h}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2x}{x(x+h)}-\frac{2(x+h)}{x(x+h)}}{h}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2x-2(x+h)}{x(x+h)}}{h}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{2x-2x-2h}{x(x+h)}}{h}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{\frac{-2h}{x(x+h)}}{h}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{-2h}{xh(x+h)}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \lim_{h \to 0}\left(\frac{-2}{x(x+h)}\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \frac{-2}{x(x+0)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{h \to 0}\left(\frac{f(x+h)-f(x)}{h}\right) = \frac{-2}{x^2}\">\r<BR>\n" );
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document.write( "Therefore, the derivative of f(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F%28x%5E2%29 ALIGN=MIDDLE  ALT=\"-2%2F%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in x = -2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F%28%28-2%29%5E2%29=-2%2F%284%29+=+-1%2F2 ALIGN=MIDDLE  ALT=\"-2%2F%28%28-2%29%5E2%29=-2%2F%284%29+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'll let you do the other problem. </SPAN>\n" );
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