document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=642347>Question 642347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> evaluate  lim h tendin  to 0 root of x+h - root x/ h  , x is not equal to 0<BR>\n" );
document.write( "sir / maam humble requestsolve  my  problem pls<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404122 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=404122\">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( "The trick here is to deny our instincts and rationalize the <i><b>numerator</b></i>\r<BR>\n" );
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document.write( "Note that the numerator is the difference of two quantities that we would very much like to square individually.  Recalling that the product of a pair of conjugates is the difference of two squares, multiply the fraction by 1 in the form of the conjugate of the numerator divided by itself:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\rightarrow{h}}\,\left( \frac{\sqrt{x\ +\ h}\ -\ \sqrt{x} }{h}\right)\left(\frac{\sqrt{x\ +\ h}\ +\ \sqrt{x}}{\sqrt{x\ +\ h}\ +\ \sqrt{x}}\right)\ =\ \lim_{x\rightarrow{h}}\,\frac{x\ +\ h\ -\ x}{h\left(\sqrt{x\ +\ h}\ +\ \sqrt{x})}\ =\ \lim_{x\rightarrow{h}}\,\frac{h}{h\left(\sqrt{x\ +\ h}\ +\ \sqrt{x}\right)}\ =\ \lim_{x\rightarrow{h}}\,\frac{1}{\left(\sqrt{x\ +\ h}\ +\ \sqrt{x}\right)\">\r<BR>\n" );
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document.write( "Now all you have to do is drive <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE h\"> to zero:\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}}\">\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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