document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118241>Question 1118241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a. HINT [See Example 2.] (If there is no such value, enter NONE.)<BR>\n" );
document.write( "f(x) =  2-2e^x/x; a=0\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733521 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=733521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A couple of preliminary comments....<br><BR>\n" );
document.write( "(1) Do you really think it is any help to us to include \"HINT [See Example 2.]\" in your message to us?!<br><BR>\n" );
document.write( "(2) The problem as you show it is of little interest, because it is impossible to define f(a) to make f continuous at x=0:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29+=+2-2e%5E0%2F0+=+2-1%2F0 ALIGN=MIDDLE  ALT=\"f%280%29+=+2-2e%5E0%2F0+=+2-1%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is undefined.<br><BR>\n" );
document.write( "If you are working on a problem like this, then your knowledge of mathematics should be sufficient that you would know appropriate use of parentheses is critical.<br><BR>\n" );
document.write( "The function you are asking about is, in fact, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%282-2e%5Ex%29%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29+=+%282-2e%5Ex%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >; not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2-2e%5Ex%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29+=+2-2e%5Ex%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "At x=0, the function value is the indeterminate form 0/0.<br><BR>\n" );
document.write( "So use l'Hospital's rule.<br><BR>\n" );
document.write( "limit as x approaches 0 of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-2e%5Ex%29%2Fx ALIGN=MIDDLE  ALT=\"%282-2e%5Ex%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "is equal to<br><BR>\n" );
document.write( "limit as x approaches 0 of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2e%5Ex%2F1 ALIGN=MIDDLE  ALT=\"-2e%5Ex%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -2e^0 = -2<br><BR>\n" );
document.write( "A graphing calculator will confirm this answer.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-10%2C2%2C%282-2e%5Ex%29%2Fx%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-10%2C2%2C%282-2e%5Ex%29%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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