This exercise is intended to reinforce the proof of Taylors Theorem. (a) Show that f(x) = To(x)

This exercise is intended to reinforce the proof of Taylor’s Theorem.

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(a) Show that f(x) = To(x) + + -S* f'(u)du. (b) Use Integration by Parts to prove the formula ~x (x-u)f(²)(u) du = -f'(a)(x-a) + + f²f' (u) du a (c) Prove the case n = 2 of Taylor's Theorem: f(x) = T₁(x) + f(x - u) f²) (u) du a