This exercise is intended to reinforce the proof of Taylor's Theorem. (a) Show that f(x) = To(x) + f'(u) du. (b) Use Integration by Parts
This exercise is intended to reinforce the proof of Taylor's Theorem. (a) Show that f(x) = To(x) + f'(u) du. (b) Use Integration by Parts to prove the formula (x - u)f (u) du = -f'(a)(x - a)+/ f'(u) du (c) Prove the case n = 2 of Taylor's Theorem: f (x) = Ti(x)+ (x - u)f (u) du
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