document.write( "Question 198498: lim 4x-1/8X^2+3X+1
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Algebra.Com's Answer #149030 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Edwin's solution.\r\n" );
document.write( "Stanbon is right. You are finding the horizontal asymptote.  Here's\r\n" );
document.write( "a little more detailed way to look at it. \r\n" );
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document.write( " lim \"%284x-1%29%2F%288x%5E2%2B3x%2B1%29\"\r\n" );
document.write( "x->OO \r\n" );
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document.write( "Finding the limit of a rational function as x approaches infinity depends\r\n" );
document.write( "on this theorem that we accept on faith:\r\n" );
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document.write( "limx->oo\"k%2Fx%5En\" = 0, if n>0 and k is any constant.\r\n" );
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document.write( "Method: Divide every term on top and bottom of \"%284x-1%29%2F%288X%5E2%2B3X%2B1%29\"\r\n" );
document.write( "by the largest power of x that appears in there.\r\n" );
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document.write( "So,\r\n" );
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document.write( "limx->oo\"%284x-1%29%2F%288x%5E2%2B3x%2B1%29%29\" \r\n" );
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document.write( "becomes\r\n" );
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document.write( "limx->oo\"%284x%2Fx%5E2-1%2Fx%5E2%29%2F%288x%5E2%2Fx%5E2%2B3x%2Fx%5E2%2B1%2Fx%5E2%29%29\" \r\n" );
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document.write( "and upon simplifying the fractions, you have:\r\n" );
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document.write( "limx->oo\"%284%2Fx-1%2Fx%5E2%29%2F%288%2B3%2Fx%2B1%2Fx%5E2%29%29\"\r\n" );
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document.write( "Now every term on top approaches 0 as x approaches infinity.\r\n" );
document.write( "So the whole numerator approaches 0.  \r\n" );
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document.write( "And the two terms of the denominator other than the 8 both\r\n" );
document.write( "approack 0, and so, the fraction approaches \"%280-0%29%2F%288%2B0%2B0%29=0%2F8=0\" \r\n" );
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document.write( "So the limit is 0.\r\n" );
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document.write( "Note:\r\n" );
document.write( "[Note here that the denominator did not approach \r\n" );
document.write( "0 too, and we were saved from having to face that dilemma \r\n" );
document.write( "of having both a numerator and a denominator approach 0.\r\n" );
document.write( "But that dilemma occurs in other problems you'll be studying.]\r\n" );
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document.write( "Edwin
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