document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090027>Question 1090027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help \r<BR>\n" );
document.write( "\n" );
document.write( "f(x)=(x²-4)/|x-2| find each limit (if possible)\r<BR>\n" );
document.write( "\n" );
document.write( "a) lim as x&#8594;2 from left f(x)\r<BR>\n" );
document.write( "\n" );
document.write( "b)lim as x&#8594;2 from right f(x)\r<BR>\n" );
document.write( "\n" );
document.write( "c)lim as x&#8594;2 f(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704702 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The function is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2-4%29%2Fabs%28x-2%29 ALIGN=MIDDLE  ALT=\"y=%28x%5E2-4%29%2Fabs%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B2%29%2A%28x-2%29%2Fabs%28x-2%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B2%29%2A%28x-2%29%2Fabs%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The function is clearly undefined at x=2, since the denominator will be 0.  The limit as x approaches 2 will exist if and only if the limits as you approach 2 both from the left and from the right are the same.\r<BR>\n" );
document.write( "\n" );
document.write( "For values of x less than 2, |x-2| = -(x-2), so\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2Fabs%28x-2%29+=+-1 ALIGN=MIDDLE  ALT=\"%28x-2%29%2Fabs%28x-2%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so the function is equivalent to -(x+2), or\r<BR>\n" );
document.write( "\n" );
document.write( "  f(x) = -x-2\r<BR>\n" );
document.write( "\n" );
document.write( "So as you approach 2 from the left, the function value approaches\r<BR>\n" );
document.write( "\n" );
document.write( "  -2-2 = -4\r<BR>\n" );
document.write( "\n" );
document.write( "For values of x greater than 2, |x-2| = (x-2), so\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2Fabs%28x-2%29+=+1 ALIGN=MIDDLE  ALT=\"%28x-2%29%2Fabs%28x-2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so the function is equivalent to\r<BR>\n" );
document.write( "\n" );
document.write( "  f(x) = 1(x+2) = x+2\r<BR>\n" );
document.write( "\n" );
document.write( "So as you approach 2 from the left, the function value approaches\r<BR>\n" );
document.write( "\n" );
document.write( "  2+2 = 4\r<BR>\n" );
document.write( "\n" );
document.write( "So the answers are\r<BR>\n" );
document.write( "\n" );
document.write( "  a) the limit as x approaches 2 from the left is -4<BR>\n" );
document.write( "  b) the limit as x approaches 2 from the right is 4<BR>\n" );
document.write( "  c) the limit as x approaches 2 does not exist, because the limits from<BR>\n" );
document.write( "       the left and right are not the same<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );