Math 257/316, Midterm 2, Section 10117 November 2006Instructions.The duration of the exam is 55 minutes. Answer all questions. Calculators are not allowed.Maximum score 100.1. Letf(x)=cos(2x)(a) Determine thesineseries expansion forf(x)on the interval0<x<π.(b) Is the Fourier series forf(x)on the interval−ππthe same expansion as you found abovein part (a)? Is there a way to answer this without working out the expansion?Hint:It may be useful to know thatπZ0sin(nx)cos(2x)dx=½0ifnis even2nn2−
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