document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977471>Question 977471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! <BR>\n" );
document.write( "How do I graph f(x)=(x^2-1)/(x+1)?<BR>\n" );
document.write( "What does lim(x->1) (x^2-1)/(x+1) equal?\r<BR>\n" );
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document.write( "I graphed the function with a discontinuity at x=-1, but I'm not sure how my second question relates? Doesn't the limit have to be approaching an aymptote? Since it is approaching 1, I think y=0. I don't understand how that is possible if x=1 is not a discontinuity. My book says that there is a hole at x=1, but I have tried graphing it on a calculator and cannot seem to find it.\r<BR>\n" );
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document.write( "Thank you very much!\r<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 #599024 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=599024\">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 graph is a straight line that has the same solution set as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ x\ -\ 1\"> except for the discontinuity, \"hole\" if you will, at the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (-1, -2)\"> because the denominator of the original function is zero when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ -1\">.\r<BR>\n" );
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document.write( "The original function is continuous at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 1\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \lim_{x\right 1}\,\frac{x^2\ -\ 1}{x\ +\ 1}\"> is simply the value of the function at 1.\r<BR>\n" );
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document.write( "A limit can be taken at any value and that value does not necessarily have to be in the domain of the function.  Review the definition of a limit:\r<BR>\n" );
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document.write( "<i>Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\"> be a function defined on an interval that contains <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ a\">, <u>except possibly at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \under {x\ =\ a}\">,</u> then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\right a}\,f(x)\ =\ L\"> \r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \forall\ \epsilon\ \in\ \mathbb{R}\ >\ 0\ \exists\ \delta\ \in\ \mathbb{R}\ >\ 0\"> such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large |f(x)\ -\ L|\ <\ \epsilon\"> whenever <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large |x\ -\ a|\ <\ \delta\"></i>\r<BR>\n" );
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document.write( "I'm quite surprised that the question asked you for the limit at 1, a very trivial and uninteresting question indeed.  I wouldn't be surprised to find out that when you went back and checked your assignment that the limit of interest is actually the limit as x goes to -1.\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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