document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=311326>Question 311326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find f(a+h)-f(a)/h for f(x)=x^2+3x+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #222662 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=222662\">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 \ \ \ \ \ \ \ \ \ \ f(x)\ =\ x^2\ +\ 3x\ +\ 1\">\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(a)\"> is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(a)\ =\ a^2\ +\ 3a\ +\ 1\">\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(a\ +\ h)\"> is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(a\ +\ h)\ =\ (a\ +\ h)^2\ +\ 3(a\ +\ h)\ +\ 1\">\r<BR>\n" );
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document.write( "so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{f(a\ +\ h)\ -\ f(a)}{h}\ =\ \frac{\left((a\ +\ h)^2\ +\ 3(a\ +\ h)\ +\ 1\right)\ -\ \left(a^2\ +\ 3a\ +\ 1\right)}{h}\">\r<BR>\n" );
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document.write( "Expanding the binomials:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{f(a\ +\ h)\ -\ f(a)}{h}\ =\ \frac{\left(a^2\ +\ 2ah\ +\ h^2\ +\ 3a\ +\ 3h\ +\ 1\right)\ -\ \left(a^2\ +\ 3a\ +\ 1\right)}{h}\">\r<BR>\n" );
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document.write( "Removing parentheses and collecting like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{f(a\ +\ h)\ -\ f(a)}{h}\ =\ \frac{2ah\ +\ h^2\ +\ 3h}{h}\">\r<BR>\n" );
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document.write( "Then eliminating the factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\"> common to both numerator and denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{f(a\ +\ h)\ -\ f(a)}{h}\ =\ 2a\ +\ h\ +\ 3\">\r<BR>\n" );
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document.write( "And that's all there is to it.\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" );
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