document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161387>Question 1161387</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider:<BR>\n" );
document.write( "f(x)=(x^2-3x-4)/(x^2-16)\r<BR>\n" );
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document.write( "Give the domain of f(x).\r<BR>\n" );
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document.write( "Test all the conditions of continuity to determine whether the given function is continuous of discontinuous at point x=4.<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 #784921 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=784921\">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=%28x%5E2-3x-4%29%2F%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2-3x-4%29%2F%28x%5E2-16%29\"   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=f%28x%29=%28%28x+%2B+1%29+%28x+-+4%29%29%2F%28%28x-4%29%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28%28x+%2B+1%29+%28x+-+4%29%29%2F%28%28x-4%29%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The function domain:\r<BR>\n" );
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document.write( "all values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > except those which make denominator equal to zero and these are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "so,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-4 ALIGN=MIDDLE  ALT=\"x+%3C+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3C+x+%3C+4 ALIGN=MIDDLE  ALT=\"-4+%3C+x+%3C+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+4 ALIGN=MIDDLE  ALT=\"x+%3E+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "interval notation:\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity+ ALIGN=MIDDLE  ALT=\"-infinity+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) U (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) U (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity+ ALIGN=MIDDLE  ALT=\"infinity+\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " to determine whether a function is continuous at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is excluded from domain because it makes 0 in the denominator, a function is NOT continuous at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to determine whether a function is continuous at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > check the limit:<BR>\n" );
document.write( "the limit of the function as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > approaches the value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=must ALIGN=MIDDLE  ALT=\"must\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=exist ALIGN=MIDDLE  ALT=\"exist\"   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=f%28x%29=%28%28x+%2B+1%29+%28x+-+4%29%29%2F%28%28x-4%29%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28%28x+%2B+1%29+%28x+-+4%29%29%2F%28%28x-4%29%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x+%2B+1%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x+%2B+1%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find limit\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E4%2C%28x+%2B+1%29%2F%28x%2B4%29%29=%284+%2B+1%29%2F%284%2B4%29=5%2F8 ALIGN=MIDDLE  ALT=\"lim%28x-%3E4%2C%28x+%2B+1%29%2F%28x%2B4%29%29=%284+%2B+1%29%2F%284%2B4%29=5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a function IS continuous at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   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=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%5E2-3x-4%29%2F%28x%5E2-16%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%5E2-3x-4%29%2F%28x%5E2-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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