document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987872>Question 987872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E3+%2B+11+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E3+%2B+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+3+ ALIGN=MIDDLE  ALT=\"+a+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Find and simplify the quotient:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%29-f%28a%29%29%2F%28x+-+a%29 ALIGN=MIDDLE  ALT=\"%28f%28x%29-f%28a%29%29%2F%28x+-+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=\r<BR>\n" );
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document.write( "Then find the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+++M_a+++ ALIGN=MIDDLE  ALT=\"+++M_a+++\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the line tangent to the graph of f at the point (a,f(a))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M_a ALIGN=MIDDLE  ALT=\"M_a\"   DISABLED_style= \"max-width:90%; height:auto;\" >=\r<BR>\n" );
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document.write( "Please give details on how this is solved very confused.\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #608594 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=608594\">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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  f(x)\ =\ x^3\ +\ 11\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{f(x)\ -\ f(a)}{x\ -\ a}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{(x^3\ +\ 11)\ -\ (a^3\ +\ 11)}{x\ -\ a\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{x^3\ -\ a^3}{x\ -\ a}\">\r<BR>\n" );
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document.write( "Recall the factorization of the difference of two cubes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{(x\ -\ a)(x^2\ +\ ax\ +\ a^2)}{x\ -\ a}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  x^2\ +\ ax\ +\ a^2\">\r<BR>\n" );
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document.write( "Now you can take the limit as x approaches a:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \lim_{x\right{a}}\,x^2\ +\ ax\ +\ a^2\ =\ a^2\ +\ a^2\ +\ a^2\ =\ 3a^2\">\r<BR>\n" );
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document.write( "Therefore\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ M_a\ =\ 3a^2\">\r<BR>\n" );
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document.write( "Hence, at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ =\ 3\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ M_{a=3}\ =\ 3(3)^2\ =\ 27\">\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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