document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198498>Question 198498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> lim   4x-1/8X^2+3X+1<BR>\n" );
document.write( "->OO \r<BR>\n" );
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document.write( "what is the trick to this<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 #149023 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=149023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> lim 4x-1/8X^2+3X+1<BR>\n" );
document.write( "->OO <BR>\n" );
document.write( "what is the trick to this<BR>\n" );
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document.write( "Since x is getting larger without bound, <BR>\n" );
document.write( "it certainly is not zero.<BR>\n" );
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document.write( "So divide numerator and denominator by x^2 to get:<BR>\n" );
document.write( "{[4x-1]/x^2}/{[8x^2+3x+1]/x^2<BR>\n" );
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document.write( "Expand that to get:<BR>\n" );
document.write( "{(4/x - 1/x^2)] / [8 + 3/x + 1/x^2]<BR>\n" );
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document.write( "Take the limit of that as x goes to infinity.<BR>\n" );
document.write( "Notice that the fractions with x in the denominator<BR>\n" );
document.write( "approach zero as x approaches infinity.<BR>\n" );
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document.write( "The limit is (0 - 0)/(8 + 0 + 0) = 0/8 = 0<BR>\n" );
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document.write( "Hope that helps.<BR>\n" );
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document.write( "what you are really finding is the horizontal asymptote.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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