Test- a 45.pdf - comparing with the corresponding deriva...

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comparing with the corresponding deriva- tive of f at a. This time, the error in the nth-degree polynomial approximation P(x) can be estimated by the following generalization of the MVT. Proposition 4.25 (Taylor Theorem). Let a, b R with a < b. Also, let n be a nonnegative integer and let f : [a, b] R be a continuous function such that
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f ,f ′′ ,...,f (n) exist on [a,b] and further, f (n) is differentiable on (a,b). Then there is c (a, b) such that f (b) = f (a) + f (a)(b a) + · · · + f (n) (a) (b a) n +
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