document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=944970>Question 944970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not sure how to work this out. I would appreciate any help. Thanks!\r<BR>\n" );
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document.write( "Let \"c\" be a number and consider the function f(x) = { ax^2 -5, if x <1<BR>\n" );
document.write( "                                                                                   c, if x =1<BR>\n" );
document.write( "                                                                                  (1/x)-2a, if x > 1 }\r<BR>\n" );
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document.write( "a) Find all numbers for \"a\" such that lim x-> 1 f(x) exists\r<BR>\n" );
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document.write( "b) Is there a number \"c\" such that f(x) is continuous at x=1? <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 #576294 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=576294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the limit to exist, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as you approach from the left (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C1 ALIGN=MIDDLE  ALT=\"x%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) must equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as you approach from the right <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=1 ALIGN=MIDDLE  ALT=\"x%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2-5=1%2Fx-2a ALIGN=MIDDLE  ALT=\"ax%5E2-5=1%2Fx-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%29%5E2-5=1%2F1-2a ALIGN=MIDDLE  ALT=\"a%281%29%5E2-5=1%2F1-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-5=1-2a ALIGN=MIDDLE  ALT=\"a-5=1-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a=6 ALIGN=MIDDLE  ALT=\"3a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For it to be continuous then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=2 ALIGN=MIDDLE  ALT=\"c=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That way the limit from the left, the limit from the right and the value at x=1 are all the same which is the definition of continuous.\r<BR>\n" );
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