Exercise 1.3:Find the second Taylor polynomial P₂(x) for the function f(x) = e* cos(x)about to = 0.-(a) For 0 ≤ x ≤ 0.5, find upper bound for the error between P₂(x) and f(x)(f(x) - P₂(x)) using the error formula, and compare it to the actual error.(b) For 0 ≤ x ≤ 1.0, find upper bound for the error between P₂(x) and f(x)(|ƒ(x) – P₂(x)|) using the error formula. Compare it to the actual error.(c) Approximate f f(x)dx using f P₂(x)dx.(d) Find an upper bound for the error in (c) using R2₂(x)|dx, and compareit to the actual error.Part solution to the above exercise is shown in Fig. 1.4.

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Find the second Taylor polynomial P₂(x) for the function f(x) about xo = 0. = e cos(x) (a) For 0 ≤ x ≤ 0.5, find upper bound for the error between P₂(x) and f(x) (|f(x) – P₂(x)|) using the error formula, and compare it to the actual error. (b) For 0 ≤ x ≤ 1.0, find upper bound for the error between P₂(x) and f(x) (|f(x) – P₂(x)|) using the error formula. Compare it to the actual error. (c) Approximate [ f(x) dx using ¹²P₂(x) dx.

Find the second Taylor polynomial P₂(x) for the function f(x) about xo = 0. = e cos(x) (a) For 0 ≤ x ≤ 0.5, find upper bound for the error between P₂(x) and f(x) (|f(x) – P₂(x)|) using the error formula, and compare it to the actual error. (b) For 0 ≤ x ≤ 1.0, find upper bound for the error between P₂(x) and f(x) (|f(x) – P₂(x)|) using the error formula. Compare it to the actual error. (c) Approximate [ f(x) dx using ¹²P₂(x) dx.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 36E

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