document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975670>Question 975670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the function f(x)=SqRt(x+1) find the difference quotient and simplify. \r<BR>\n" );
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document.write( "Now i have found the difference quotient to be [SqRt(x+h+1)-SqRt(x+1)]/h and when i simplify that i just rearrange the variables so that h is before x. <BR>\n" );
document.write( "But im pretty sure that simplifying a difference quotient means rationalizing the numerator in which case i got <BR>\n" );
document.write( "h/[h(SqRtx+h+1) + h(SqRtx+1)] or cancel out the h's to get <BR>\n" );
document.write( "1/SqRt(x+h+1) + Sqrt(x+1). \r<BR>\n" );
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document.write( "But im not sure which one would be correct in the simplified form if the difference quotient is in fact the same as what i got. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597360 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=597360\">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( "Yep, you did it correctly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sqrt{x\ +\ h\ +\ 1}\ -\ sqrt{x\ +\ 1}}{h}\">\r<BR>\n" );
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document.write( "When you rationalize the numerator, you end up with the difference of two squares in the numerator and a new factor in the denomiator that is the conjugate of the numerator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ +\ h\ +\ 1\ -\ (x\ +\ 1)}{h(\sqrt{x\ +\ h\ +\ 1}\ +\ sqrt{x\ +\ 1})}\">\r<BR>\n" );
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document.write( "And finally:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{\sqrt{x\ +\ h\ +\ 1}\ +\ sqrt{x\ +\ 1}}\">\r<BR>\n" );
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document.write( "which becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{2\sqrt{x\ +\ 1}}\">\r<BR>\n" );
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document.write( "when you take the limit as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\right 0\">\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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