document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=989973>Question 989973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I keep getting 0 as my answer for this problem, but the answer key says 1/2. Any help would be greatly appreciated!!\r<BR>\n" );
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document.write( "Problem: Limit as x is approaching 0 of { {sqrt ( 1+x ) -1 } / ( x ) } </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #610121 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=610121\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Do you know and did you learn that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281+%2B+x%29 ALIGN=MIDDLE  ALT=\"sqrt%281+%2B+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+%281%2F2%29x ALIGN=MIDDLE  ALT=\"1+%2B+%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > + the terms of lower orders of magnitude at &nbsp;&nbsp;x ---> 0 ?\r<BR>\n" );
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document.write( "In any case, &nbsp;it is so. \r<BR>\n" );
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document.write( "Therefore, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281+%2B+x%29-1 ALIGN=MIDDLE  ALT=\"sqrt%281+%2B+x%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x ALIGN=MIDDLE  ALT=\"%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > + the terms of lower orders of magnitude at &nbsp;&nbsp;x ---> 0, &nbsp;&nbsp;&nbsp;&nbsp;and further\r<BR>\n" );
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document.write( "&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%281+%2B+x%29-1%29%2Fx ALIGN=MIDDLE  ALT=\"%28sqrt%281+%2B+x%29-1%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + the terms of lower orders of magnitude at &nbsp;&nbsp;x ---> 0.\r<BR>\n" );
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document.write( "It implies that lim <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%281+%2B+x%29-1%29%2Fx ALIGN=MIDDLE  ALT=\"%28sqrt%281+%2B+x%29-1%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <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;\" > at &nbsp;&nbsp;x ---> 0.\r<BR>\n" );
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