document.write( "Question 1200105: For what value(s) of a and b is the function f(x) given below continuous at 0?\r
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Algebra.Com's Answer #834139 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The 3 parts of the graphs are \r\n" );
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document.write( "\"y=sin%283x%29%2Fx\", \"y=a\", \"y=%285-sqrt%2825-x%29%29%2F%28bx%29\"\r\n" );
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document.write( "The first function must approach the same value as the second function as x approaches 0 from the left. So\r\n" );
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document.write( "\"lim%5B%22x-%3E0-%22%5D\"\"%28sin%283x%29%2Fx%29\"\"%22%22=%22%22\"\"lim%5B%22x-%3E0%22%5D\"\"3%2A%28sin%283x%29%2F%283x%29%29\"\"%22%22=%22%22\"\"3%2Alim%5B%22x-%3E0%22%5D\"\"%28sin%283x%29%2F%283x%29%29\"\"%22%22=%22%22\"\"3%2A%281%29\"\"%22%22=%22%22\"\"3\"\r\n" );
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document.write( "Therefore a = 3, so the second function is y=3\r\n" );
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document.write( "Also the third function must approach the same value as the second function as\r\n" );
document.write( "x approaches 0 from the right.\r\n" );
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document.write( "\"lim%5B%22x-%3E0%2B%22%5D\"\"%28%285-sqrt%2825-x%29%29%2F%28bx%29%29\"\"%22%22=%22%22\"\"lim%5B%22x-%3E0%2B%22%5D\"\"%22%22=%22%22\"\r\n" );
document.write( "\"lim%5B%22x-%3E0%2B%22%5D\"\"%28%2825-%2825-x%29%29%2F%28bx%285%2Bsqrt%2825-x%29%29%29%29%29\"\"%22%22=%22%22\"\"lim%5B%22x-%3E0%2B%22%5D\"\"%2825-25%2Bx%29%2F%28bx%285%2Bsqrt%2825-x%29%29%29%29%29\"\"%22%22=%22%22\"\"lim%5B%22x-%3E0%2B%22%5D\"\"%28x%29%2F%28bx%285%2Bsqrt%2825-x%29%29%29%29%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\"lim%5B%22x-%3E0%2B%22%5D\"\"cross%28x%29%2F%28b%2Across%28x%29%285%2Bsqrt%2825-x%29%29%29%29%29\"\"%22%22=%22%22\"\"lim%5B%22x-%3E0%2B%22%5D\"\"1%2F%28b%2A%285%2Bsqrt%2825-x%29%29%29%29%29\"\"%22%22=%22%22\"\"1%2F%28b%2A%285%2Bsqrt%2825-0%29%29%29%29%29\"\"%22%22=%22%22\"\"1%2F%28b%2A%285%2Bsqrt%2825%29%29%29%29%29\"\"%22%22=%22%22\"\"1%2F%28b%2A%285%2B5%29%29%29%29\"\"%22%22=%22%22\"\"1%2F%2810b%29\"\r\n" );
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document.write( "So \"1%2F%2810b%29\"\"%22%22=%22%22\"\"3\"\r\n" );
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document.write( "\"1\"\"%22%22=%22%22\"\"30b\"\r\n" );
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document.write( "\"1%2F30\"\"%22%22=%22%22\"\"b\"\r\n" );
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document.write( "Here's the graph of the continuous function:\r\n" );
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document.write( "Edwin
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