UseDefinition - Mathematics 115 F2011 Example Problem Let...

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Mathematics 115 – F2011 - Example Problem Let f ( x ) = x . (1) Use the definition of the derivative to find f 0 ( x ): From the definition f 0 ( x ) = lim h 0 f ( x + h ) - f ( x ) h = lim h 0 x + h - x h provided the limit exists. Simplify the difference quotient: x + h - x h = x + h - x h · x + h + x x + h + x = x + h - x h ( x + h + x ) = 1 x + h + x Then. replacing the difference quotient with its simplified version, we get f 0 ( x ) = lim h 0 1 x
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