Solved: Fresnel integrals The theory of optics gives rise
Chapter 9, Problem 79(choose chapter or problem)
Fresnel integrals The theory of optics gives rise to the two Fresnel integrals S1x2 = L x 0 sin t2 dt and C1x2 = L x 0 cos t2 dt. a. Compute S_1x2 and C_1x2. 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 S10.052 and C1-0.252. d. How many terms of the Maclaurin series are required to approximate S10.052 with an error no greater than 10-4? e. How many terms of the Maclaurin series are required to approximate C1-0.252 with an error no greater than 10-6?
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