3.2.10-eg-1 - Example Let f(x = 2x2 4 Use the alternative...

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Unformatted text preview: Example Let f (x) = 2x2 + 4 . Use the alternative definition of the derivative, f (x) = z→x lim f (z ) − f (x) z−x . to find f (x) for this function. Solution: Using the definition of the derivative in (1), (2z 2 + 4) − (2x2 + 4) z−x 2 2 (z − x2 ) = lim z →x z−x 2(z − x)(z + x) = lim z →x z−x = z→x 2(z + x) lim f (x) = z→x lim = 2(x + x) so that we have f (x) = 4x. (1) ...
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.

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