M257_316_Midterm2_sec101W2006 - Math 257/316 Midterm 2...

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Math 257/316, Midterm 2, Section 101 17 November 2006 Instructions. The duration of the exam is 55 minutes. Answer all questions. Calculators are not allowed. Maximum score 100. 1. Let f ( x )=cos(2 x ) (a) Determine the sine series expansion for f ( x ) on the interval 0 <x< π . (b) Is the Fourier series for f ( x ) on the interval π π the same expansion as you found above in part (a)? Is there a way to answer this without working out the expansion? Hint: It may be useful to know that π Z 0 sin( nx )cos(2 x ) dx = ½ 0 if n is even 2 n n 2
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