document.write( "Question 1195064: Find the value of the constant k that makes the function continuous.
\n" ); document.write( "g(x)={2x^2-3x-20/x-4 if x≠4
\n" ); document.write( "{kx-15 if x=4
\n" ); document.write( "k=
\n" ); document.write( "thanks for all your help! \n" ); document.write( "

Algebra.Com's Answer #827405 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the value of the constant k that makes the function continuous.
\n" ); document.write( "g(x)={2x^2-3x-20/x-4 if x≠4
\n" ); document.write( "{kx-15 if x=4
\n" ); document.write( "k=
\n" ); document.write( "thanks for all your help!
\n" ); document.write( "~~~~~~~~~~~~~~~\r
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document.write( "First try to calculate the quadratic polynomial in the numerator at x= 4.\r\n" );
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document.write( "Its value is  2*4^2 - 3*4 - 20 = 2*16 - 12 - 20 = 32 - 12 - 20 = 0.\r\n" );
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document.write( "It tells you that the quadratic polynomial has the binomial (x-4) as a factor,\r\n" );
document.write( "due to the Remainder theorem.\r\n" );
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document.write( "So, try to factorize the quadratic polynomial in the numerator.\r\n" );
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document.write( "You will get 2x^2 - 3x - 20 = (x-4)*(2x+5).\r\n" );
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document.write( "Therefore, the rationsl function  g(x) =  =  = 2x+5.\r\n" );
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document.write( "It tells you that g(x), although has a hole at x= 4, nethertheless has a limit 2*4+5 = 13 at x ---> 4.\r\n" );
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document.write( "So we should take \"k\" in the expression kx-15 to get the value 13 at x=4:\r\n" );
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document.write( "    k*4 - 15 = 13,\r\n" );
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document.write( "or\r\n" );
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document.write( "    4k = 13 + 15 = 28\r\n" );
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document.write( "     k           = 28/4 = 7.\r\n" );
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document.write( "ANSWER.  k = 4.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with full explanations provided.\r
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