The theory of optics gives rise to the two Fresnel integrals a. Compute S'(x) and C'(x). b.

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The theory of optics gives rise to the two Fresnel integrals

sin t² dt and C(x) cos t dt. S(x)

a. Compute S'(x) and C'(x).

b. Expand sin t² and cos t² in a Maclaurin series and then integrate to find the first four nonzero terms of the Maclaurin series for S and C.

c. Use the polynomials in part (b) to approximate S(0.05) and C(-0.25).

d. How many terms of the Maclaurin series are required to approximate S(0.05) with an error no greater than 10^-4?
e. How many terms of the Maclaurin series are required to approximate C(-0.25) with an error no greater than 10^-6?

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Question Posted: Apr 13, 2019 09:18 AM

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The theory of optics gives rise to the two Fresnel integrals a. Compute S'(x) and C'(x). b.

Question:

sin t² dt and C(x) cos t dt. S(x)

Step by Step Answer:

a By the Fundamental Theorem Sx sin r Cx cos x b Th...View the full answer

Calculus Early Transcendentals

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