document.write( "Question 834962: Limx>2 x^3-x^2-x-2/x^2-6x+8 and limx>2 x^4-8x^2+16/x^3-3x^2+4 \n" ); document.write( "

Algebra.Com's Answer #503268 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "For limits of rational expressions, i.e. \"\"\r\n" );
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document.write( "1. Substitute what x approaches.  If the denominator is not 0. \r\n" );
document.write( "   what you get is the answer, and you're done.\r\n" );
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document.write( "2. If the denominator is 0, and the numerator is not 0, then the    \r\n" );
document.write( "   answer is  if the numerator is positive and \r\n" );
document.write( "   if the numerator is negative, and you're done.\r\n" );
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document.write( "3.  If the numerator is also 0, factor numerator and denominator and\r\n" );
document.write( "    cancel all common factors. \r\n" );
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document.write( "4. Substitute what x approaches, simplify, and what you get is the answer.\r\n" );
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document.write( "------------------------\r\n" );
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document.write( "1.  . Both\r\n" );
document.write( "    numerator and denominator are 0, so we go to step 3.\r\n" );
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document.write( "3.  Factor the numerator: Candidates for zeros are ±1,±2\r\n" );
document.write( "     has 1 sign change, so it has one \r\n" );
document.write( "    positive zero.  We try 1:\r\n" );
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document.write( "    1|1 -1 -1 -2\r\n" );
document.write( "     |   1  0 -1   \r\n" );
document.write( "      1  0 -1 -3  So 1 is not a zero\r\n" );
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document.write( "    We try 2\r\n" );
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document.write( "    2|1 -1 -1 -2\r\n" );
document.write( "     |   2  2  2   \r\n" );
document.write( "      1  1  1  0  So 2 is a zero, so the numerator factors\r\n" );
document.write( "                  as (x-2)(x²+x+1)\r\n" );
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document.write( "    The denominator x²-6x+8 factors as (x-2)(x-4)\r\n" );
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document.write( "So we have:\r\n" );
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document.write( "    \r\n" );
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document.write( "You do the other one.  The answer is \r\n" );
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document.write( "Edwin

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