The Fresnel function Ssxd y x 0 sin( 1 2t 2 ) dt was

Chapter , Problem 64

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The Fresnel function Ssxd y x 0 sin( 1 2t 2 ) dt was introduced in Section 5.3. Fresnel also used the function Csxd y x 0 cos( 1 2t 2 ) dt in his theory of the diffraction of light waves. (a) On what intervals is C increasing? (b) On what intervals is C concave upward? (c) Use a graph to solve the following equation correct to two decimal places: y x 0 cos( 1 2t 2 ) dt 0.7 (d) Plot the graphs of C and S on the same screen. How are these graphs related?

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