HW1 - Page 496 problem 11 π π π<< = x x x f is an even function 29 29 29 29 29 n n n nx nx nx n nx dx nx x a x x dx x a 1 1 1 2 sin cos 1

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Unformatted text preview: Page 496, problem 11: π π π < <-- = x x x f , ) ( is an even function. ( 29 ( 29 ( 29 ( 29 ( 29 n n n nx nx nx n nx dx nx x a x x dx x a ) 1 ( 1 1 2 ) sin( ) cos( 1 ) sin( 2 cos 2 2 2 1 1 2 2-- = ⋅ +- =- = = - =- = ∫ ∫ π π π π π π π π π π π π π π Plots of f and some partial sums: Page 496, problem 15: < < < <- = 2 2 2 ) ( x if x if x f is neither even nor odd, but if we write f(x)=1+g(x), the function g(x) is odd. Therefore ( 29 ( 29 1 1 2 2 sin 1 2 2 , 2 sin 1 ) ( 1 ) ( 2 1-- = ⋅- = ⋅ + = + = ∫ ∑ ∞ = n n n n n dx x n B x n B x g x f π π π Plots of f and some partial sums: p. 499, #9 ( 29 ( 29 ( 29 ( 29 1 1 1 1 2 2 2 1 cos 1 1 inx inx inx in in n n n inx n x c xe dx e e dx e e in in in in i n in n i f x e n π π π π π π π π π π π π π π------- ∞ =-∞ = =- + =--...
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This note was uploaded on 09/05/2011 for the course EGM 4313 taught by Professor Mei during the Spring '08 term at University of Florida.

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HW1 - Page 496 problem 11 π π π<< = x x x f is an even function 29 29 29 29 29 n n n nx nx nx n nx dx nx x a x x dx x a 1 1 1 2 sin cos 1

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