document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446017>Question 446017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use limits to describe the behavior of f(x)= 2/x^2-1  at values of x not in its domain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307136 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=307136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%282+%2F+x%5E2%29+-+1 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%282+%2F+x%5E2%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%282-+x%5E2%2F+x%5E2%29+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+%282-+x%5E2%2F+x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-%28+x%5E2-2%2F+x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%28+x%5E2-2%2F+x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Lim (x tend to -1 ) [-( x^2-2/ x^2)]=-1\r<BR>\n" );
document.write( "\n" );
document.write( " domain is R - {-1,1} as at a these points its is not defined\r<BR>\n" );
document.write( "\n" );
document.write( "taking limit at (-1). Lim (x tend to -1 ) [2 / x^2 - 1] applying L -hospital we get limit as 0 \r<BR>\n" );
document.write( "\n" );
document.write( "similar for 1\r<BR>\n" );
document.write( "\n" );
document.write( "for x from -1 to 1:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-1%2C+1%2C+-10%2C+20%2C-%28+x%5E2-2%2F+x%5E2%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-1%2C+1%2C+-10%2C+20%2C-%28+x%5E2-2%2F+x%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for x from -6 to 6:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-6%2C6%2C+-10%2C+20%2C%282-+x%5E2%29%2F+x%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-6%2C6%2C+-10%2C+20%2C%282-+x%5E2%29%2F+x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );