document.write( "Question 1073697: x^3+2x^2-x-2
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Algebra.Com's Answer #688488 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We calculate f(x+h), then f(x+h)-f(x), then \"%28f%28x%2Bh%29-f%28x%29%29%2Fh\",\r\n" );
document.write( "then \"matrix%282%2C2%2C+lim%2C%28f%28x%2Bh%29-f%28x%29%29%2Fh%2C%22h-%3E0%22%2C%22%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"x%5E3%2B2x%5E2-x-2\"\r\n" );
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document.write( "We find f(x+h):\r\n" );
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document.write( "\"%22f%28x%2Bh%29%22\"\"%22%22=%22%22\"\"%28x%2Bh%29%5E3%2B2%28x%2Bh%29%5E2-%28x%2Bh%29-2\"\r\n" );
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document.write( "\"%22f%28x%2Bh%29%22\"\"%22%22=%22%22\"\"%28x%5E3%2B3x%5E2h%2B3xh%5E2%2Bh%5E3%29%2B2%28x%5E2%2B2hx%2Bh%5E2%29-x-h-2\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%2Bh%29%22\"\"%22%22=%22%22\"\"x%5E3%2B3x%5E2h%2B3xh%5E2%2Bh%5E3%2B2x%5E2%2B4hx%2B2h%5E2-x-h-2\"\r\n" );
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document.write( "We find f(x+h)-f(x)\r\n" );
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document.write( "\"%22f%28x%2Bh%29%22-%22f%28x%29%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"%22f%28x%2Bh%29%22-%22f%28x%29%22\"\"%22%22=%22%22\"\"x%5E3%2B3x%5E2h%2B3xh%5E2%2Bh%5E3%2B2x%5E2%2B4hx%2B2h%5E2-x-h-2-x%5E3-2x%5E2%2Bx%2B2\"\r\n" );
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document.write( "We simplify and find that all terms not containing h cancel:\r\n" );
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document.write( "\"%22f%28x%2Bh%29%22-%22f%28x%29%22\"\"%22%22=%22%22\"\"3x%5E2h%2B3xh%5E2%2Bh%5E3%2B4hx%2B2h%5E2-h\"\r\n" );
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document.write( "We factor out h\r\n" );
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document.write( "\"%22f%28x%2Bh%29%22-%22f%28x%29%22\"\"%22%22=%22%22\"\"h%283x%5E2%2B3xh%2Bh%5E2%2B4x%2B2h-1%29\"\r\n" );
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document.write( "We find \"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"\r\n" );
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document.write( "\"%28%22f%28x%2Bh%29%22-%22f%28x%29%22%29%2Fh\"\"%22%22=%22%22\"\"%28h%283x%5E2%2B3xh%2Bh%5E2%2B4x%2B2h-1%29%29%2Fh\"\r\n" );
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document.write( "We cancel the h's:\r\n" );
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document.write( "\"%28%22f%28x%2Bh%29%22-%22f%28x%29%22%29%2Fh\"\"%22%22=%22%22\"\"3x%5E2%2B3xh%2Bh%5E2%2B4x%2B2h-1\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%27%28x%29%22\"\"%22%22=%22%22\"\"matrix%282%2C2%2C+lim%2C%28f%28x%2Bh%29-f%28x%29%29%2Fh%2C%22h-%3E0%22%2C%22%22%29\"\"%22%22=%22%22\"\"matrix%282%2C2%2C+lim%2C%283x%5E2%2B3xh%2Bh%5E2%2B4x%2B2h-1%29%2C%22h-%3E0%22%2C%22%22%29\"\r\n" );
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document.write( "\"%22f%27%28x%29%22\"\"%22%22=%22%22\"\"3x%5E2%2B3x%2A0%2B0%5E2%2B4x%2B2%280%29-1\"\r\n" );
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document.write( "\"%22f%27%28x%29%22\"\"%22%22=%22%22\"\"%22%22=%22%22\"\"3x%5E2%2B4x-1\"\r\n" );
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document.write( "Edwin
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