document.write( "Question 374259: find the limit as x approaches 1^+ of\r
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Algebra.Com's Answer #266365 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"matrix%282%2C1%2Clim%2C%22x-%3E1%22%5E%22%2B%22%29\"\"%28ln%28x%29%2ATan%28pi%2Ax%2F2%29%29\"\r\n" );
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document.write( "Write the tangent expression as the reciprocal of the cotangent\r\n" );
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document.write( "\"matrix%282%2C1%2Clim%2C%22x-%3E1%22%5E%22%2B%22%29\"\"%28ln%28x%29%28expr%281%2FCot%28pi%2Ax%2F2%29%29%29%29\"\r\n" );
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document.write( "which is the same as:\r\n" );
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document.write( "\"matrix%282%2C1%2Clim%2C%22x-%3E1%22%5E%22%2B%22%29\"\"%28expr%28%28ln%28x%29%29%2FCot%28pi%2Ax%2F2%29%29%29%29\"\r\n" );
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document.write( "Since both numerator and denominator approach 0 as x approaches -1,\r\n" );
document.write( "we can use L'Hopital's rule by taking deritatives of top and bottom:\r\n" );
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document.write( "[The software available here writes Csc²x as Csc²\"%22%22%2A%22%22\"x and same\r\n" );
document.write( "for other trig functions squared. Sorry! )\r\n" );
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document.write( "\"matrix%282%2C1%2Clim%2C%22x-%3E1%22%5E%22%2B%22%29\"\"%28expr%281%2Fx%29%2F%28-Csc%5E2%28pi%2Ax%2F2%29%2A%28pi%2F2%29%29%29%29%29\"\r\n" );
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document.write( "Write the cosecant squared in the denominator as a sine squared in the\r\n" );
document.write( "numerator, and remember to keep the - sign:\r\n" );
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document.write( "\"matrix%282%2C1%2Clim%2C%22x-%3E1%22%5E%22%2B%22%29\"\"%28%28-expr%281%2Fx%29%2ASin%5E2%28pi%2Ax%2F2%29%29%2F%28%28pi%2F2%29%29%29%29%29\"\r\n" );
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document.write( "Change division by \"pi%2F2\" as multiplication by its reciprocal \"2%2Fpi%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2Clim%2C%22x-%3E1%22%5E%22%2B%22%29\"\"%28-expr%281%2Fx%29%2ASin%5E2%28pi%2Ax%2F2%29%2A%282%2Fpi%29%29%29%29\"\r\n" );
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document.write( "Now when x is close to 1 this is close to what we get when we\r\n" );
document.write( "substitute 1 for x\r\n" );
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document.write( "\"-expr%281%2F%281%29%29%2ASin%5E2%28pi%2A%281%29%2F2%29%2A%282%2Fpi%29%29%29\"\r\n" );
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document.write( "\"-Sin%5E2%28pi%2F2%29%2A%282%2Fpi%29%29\"\r\n" );
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document.write( "\"-%281%29%5E2%2A%282%2Fpi%29%29\"\r\n" );
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document.write( "\"-2%2Fpi\"\r\n" );
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document.write( "Edwin
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