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File1054 - Quiz 10 Math 322 Section 4 Fall 2009 November 6...

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Unformatted text preview: Quiz 10 Math 322, Section 4. Fall, 2009. November, 6 2009. NAME: Instructor: Bole Yang Please show ALL of your work. 1. Consider the function “(EFL—1 if ——2§m<0 fi03352 which is assumed to have a period of 4. Let fix) 2 on + 2(ancos(1;r)+bnsin(%m)) n=1 be its Fourier series. Write the first four NONZERO terms of the Fourier series. ._ 2. 2. ._ 1.: \ c . wrrx - WA A?“ "“2 g?- ‘il K3 gm 2 OKX = i— . 2. £009”. d‘X 2. o .-' wu- 2 2 I n = "-2 gu ‘ "' §\‘n fi—L AX = '— """"" 0.9.; W” x z: _ —'— (f‘l) ___‘ o 1 mr T o wu- . 2. Given that f (m) is some arbitrary EVEN function with period 2L, show that the coefficients bn in its Fourier HM- _ Series all vanish identically to zero 0 L ifib —-L :QL‘GLX) $\“T "X‘ '1—(2‘c-11)§:NW“WTX‘O\9<+ g-e‘iygihvrwf‘w) 5 t‘ .K\L Lo .. i ( 2-: 7% S ‘Qb‘tw‘nhfl—B AL—tH’ Sim": ——o\x\"L Lin E hucufifn -- dt+S%X1S$‘?dM\ ...
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