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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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