document.write( "Question 1209153: If f(x)= (k+x³sec(x))/(sin(b)×(x-π)) is continuous at x= π, and kb -f(π)= 4(π^(5/ 2) , find the value of b .\r
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Algebra.Com's Answer #847783 by Edwin McCravy(20066)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You apparently meant this, for it is another L'Hopital's theorem problem from\r\n" );
document.write( "the limit section of Calc II.\r\n" );
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document.write( "If \"f%28x%29\"\"%22%22=%22%22\"\"%28k%2Bx%5E3sec%5E%22%22%28x%29%29%2F%28sin%5E%22%22%28+b%28x-pi%29+%29+%29\" is continuous at \"x=pi\", and \"kb-f%28pi%29=+4pi%5E%28%225%2F2%22%29\" , find the value of \"b\".\r\n" );
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document.write( "Since numerator and denominator both approach zero as x approaches π,\r\n" );
document.write( "L'Hopital's theorem applies and\r\n" );
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document.write( "\"f%28pi%29\"\"%22%22=%22%22\"\"matrix%282%2C1%2Clim%2Cmatrix%281%2C2%2C%22x-%3E%22%2Cpi%29%29\"\"%22%22=%22%22\"\"matrix%282%2C1%2Clim%2Cmatrix%281%2C2%2C%22x-%3E%22%2Cpi%29%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\"%22%22=%22%22\"\"%28pi%5E3%2A%28-1%29%280%29%2B%28-1%29%283pi%5E2%29%29%2F%28b%2A1%5E%22%22%29\"\"%22%22=%22%22\"\"-3pi%5E2%2Fb%5E%22%22\"\r\n" );
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document.write( "\"kb-%28-3pi%5E2%2Fb%5E%22%22%29=+4pi%5E%28%225%2F2%22%29\"\r\n" );
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document.write( "\"kb%5E2%2B3pi%5E2=+4pi%5E%28%225%2F2%22%29%2Ab\"\r\n" );
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document.write( "\"kb%5E2-4pi%5E%28%225%2F2%22%29%2Ab%2B3pi%5E2=0\"\r\n" );
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document.write( "\"b\"\"%22%22=%22%22\"\"%284pi%5E%225%2F2%22%2B-+sqrt%2816pi%5E5-12k%2Api%5E2%29%29%2F%282k%5E%22%22%29\"\r\n" );
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document.write( "\"b\"\"%22%22=%22%22\"\"%284pi%5E%225%2F2%22%2B-+sqrt%284pi%5E2%284pi%5E3-3k%29%29%29%2F%282k%5E%22%22%29\"\r\n" );
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document.write( "\"b\"\"%22%22=%22%22\"\"%284pi%5E%225%2F2%22%2B-+2pi%2Asqrt%284pi%5E3-3k%29%29%2F%282k%5E%22%22%29\"\r\n" );
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document.write( "\"b\"\"%22%22=%22%22\"\"%282pi%5E%225%2F2%22%2B-+pi%2Asqrt%284pi%5E3-3k%29%29%2F%28k%5E%22%22%29\"\r\n" );
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document.write( "That is only valid for \"4pi%5E3-3k%3E=0\" and \"k%3C%3E0\"\r\n" );
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document.write( "\"-3k%3E-4pi%5E3\"\r\n" );
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document.write( "\"3k%3C4pi%5E3\"\r\n" );
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document.write( "\"k%3Cexpr%284%2F3%29pi%5E3\" and \"k%3C%3E0\" \r\n" );
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document.write( "\"0%3C=k%3C=expr%284%2F3%29pi%5E3\"\r\n" );
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document.write( "Answer \"b\"\"%22%22=%22%22\"\"%282pi%5E%225%2F2%22%2B-+pi%2Asqrt%284pi%5E3-3k%29%29%2F%28k%5E%22%22%29\", \"0%3C=k%3C=expr%284%2F3%29pi%5E3\"\r\n" );
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document.write( "Edwin
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