This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Consider the following function. f(x) = e2x2, a = 0, n = 3, 0 ≤ x ≤ 0.1 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) + f ''(a) 2! (x − a)2 + f '''(a) 3! (x − a)3. The function f(x) = e2x2 has derivatives f '(x) = $$ Correct: Your answer is correct. 4x e2x2, f ''(x) = $$ Correct: Your answer is correct. 16x^2+4 e2x2, and f '''(x) = $$ Correct: Your answer is correct. 64x^3+48x e2x2. Step 2 With a = 0, f(0) = 1 Correct: Your answer is correct. seenKey 1 , f '(0) = 0 seenKey 0 , f ''(0) = 4 seenKey 4 , and f '''(0) = 0. Step 3 Therefore, T3(x) = . Exercise (b) Use Taylor's Inequality to estimate the accuracy of the approximation f ≈ Tn(x) when x lies in the given interval. Step 1 If |f (4)(x)| ≤ M, then we know tha