document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158629>Question 1158629</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Suppose f(x) is defined as shown below<BR>\n" );
document.write( " f(x) ={e^x if x ≥ 0 <BR>\n" );
document.write( "       {x + 1 if x < 0 <BR>\n" );
document.write( "Determine whether or not that f is continuous at 0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781582 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=781582\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose <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;\" > is defined as shown below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=e%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29+=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=0 ALIGN=MIDDLE  ALT=\"x+%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1 ALIGN=MIDDLE  ALT=\"x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+0 ALIGN=MIDDLE  ALT=\"x+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Determine whether or not that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > is continuous at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "for the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=0 ALIGN=MIDDLE  ALT=\"x+%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have to select the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29++=+e%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29++=+e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "right-hand limit:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > comes from the right, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+a ALIGN=MIDDLE  ALT=\"x+%3E+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+f%28x%29+%29=+lim+%28x-%3E0%2Ce%5Ex+%29=1 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+f%28x%29+%29=+lim+%28x-%3E0%2Ce%5Ex+%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......a)\r<BR>\n" );
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document.write( "for the values of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%3C+0 ALIGN=MIDDLE  ALT=\"+x%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have to select the function<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29++=x+%2B+1 ALIGN=MIDDLE  ALT=\"+f%28x%29++=x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "left-hand limit: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > comes from the left, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+a ALIGN=MIDDLE  ALT=\"x+%3C+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim+%28x-%3E0%2Cx%2B1%29=1 ALIGN=MIDDLE  ALT=\"lim+%28x-%3E0%2Cx%2B1%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim+%28x-%3E0%2Ce%5Ex+%29=+lim+%28x-%3E0%2Cx%2B1%29 ALIGN=MIDDLE  ALT=\"lim+%28x-%3E0%2Ce%5Ex+%29=+lim+%28x-%3E0%2Cx%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=continuous ALIGN=MIDDLE  ALT=\"continuous\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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