Let (x) sin(x 2 ) and I 1 0 (x) dx (a) Check that f'(x) 2 cos(x) 4x sin(x) Then show that f (x) 6 for x 0, 1 12 cos(x) 2 and 14x sin(x) 4 for x 0, 1 1 (b) Show that Error(MN) is at most 4N (c) Find an N such that I MN 10 ...

a Taking derivatives we get On the interval 0 1 fx 2x cosx fx 2x ...

Let (x) = sin(x 2 ) and I = 1 0 (x) dx. (a) Check that

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Let ƒ(x) = sin(x²) and I = ∫¹₀ƒ(x) dx.

(a) Check that f'(x) = 2 cos(x) - 4x sin(x). Then show that f"(x)| 6 for x = [0, 1]. 12 cos(x)| 2 and 14x

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 07, 2023 08:07 AM

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Let (x) = sin(x 2 ) and I = 1 0 (x) dx. (a) Check that

Question:

(a) Check that f'(x) = 2 cos(x²) - 4x² sin(x²). Then show that f"(x)| ≤ 6 for x = [0, 1]. 12 cos(x²)| ≤ 2 and 14x² sin(x²)| ≤ 4 for x € [0, 1]. 1 (b) Show that Error(MN) is at most 4N² (c) Find an N such that I - MN| ≤ 10-³.

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a Taking derivatives we get On the interval 0 1 fx 2x cosx fx 2x...View the full answer

Calculus

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