document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139240>Question 1139240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the indicated limit, if it exists. (2 points) <BR>\n" );
document.write( "limit of f of x as x approaches 0 where f of x equals 5 x minus 8 when x is less than 0 and the absolute value of the quantity negative 4 minus x when x is greater than or equal to 0\r<BR>\n" );
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document.write( "	<BR>\n" );
document.write( "-4<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "-12<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "-8<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "The limit does not exist.<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 #757035 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=757035\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "Piecwise Function:<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "g(x) = 5x-8<BR>\n" );
document.write( "h(x) = |4-x|\r<BR>\n" );
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document.write( "The f(x) function will change identity, so to speak, depending on what x is. There are two cases:<BR>\n" );
document.write( "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;\" >, then f(x) = g(x) = 5x-8<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "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;\" >, then f(x) = h(x) = |4-x|\r<BR>\n" );
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document.write( "Let's plug x = 0 into the g(x) function<BR>\n" );
document.write( "g(x) = 5x-8<BR>\n" );
document.write( "g(0) = 5*0-8<BR>\n" );
document.write( "g(0) = 0-8<BR>\n" );
document.write( "g(0) = -8<BR>\n" );
document.write( "The input x = 0 leads to the output y = -8. We'll use this output later, so make sure to mark it.\r<BR>\n" );
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document.write( "Now plug x = 0 into h(x)<BR>\n" );
document.write( "h(x) = |4-x|<BR>\n" );
document.write( "h(0) = |4-0|<BR>\n" );
document.write( "h(0) = |4|<BR>\n" );
document.write( "h(0) = 4<BR>\n" );
document.write( "We get an output of y = 4 here, in contrast to y = -8 earlier. Since these outputs do not match up (ie they are not equal), this means that we have a disconnect. The graph confirms this gap<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/UrtPEN6.png\"><BR>\n" );
document.write( "Therefore, the limit <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \displaystyle \lim_{x\to 0}f(x)\"> does not exist.\r<BR>\n" );
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document.write( "More formally, the left hand limit (LHL) is -8 while the right hand limit (RHL) is 4. Since the LHL and the RHL aren't the same, this means the overall limit at this x value does not exist. For a limit to exist, the two sides must meet up at the same point (even if there is a hole at this meeting point). \r<BR>\n" );
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document.write( "Final Answer: The limit does not exist (choice D)<BR>\n" );
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