Consider the following function f x 2x a 0 n 3 0 x 0 2 Exercise a Approximate f by a Taylor polynomial with degree n at the

Question

Consider the following function f x 2x a 0 n 3 0 x 0 2 Exercise a Approximate f by a Taylor polynomial with degree n at the number a Step 1 The Taylor polynomial with degree n 3 is T3 x f a f a x a The function f x 2x Step 2 f x f x f x 4x 16x 4 With a 0 f 0 has derivatives 64x 48x f 0 Submit Skip you cannot come back Step 1 If Ir 4 x M then we know that M IR x 4r a Ix 16r 4 e x 64 48 and Je x Exercise b Use Taylor s Inequality to estimate the accuracy of the approximation fx T x when x lies in the given interval f 0 and f 0 0 4

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