MATH300 Midterm: MATH 300 UofA Exam Solution 3
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Solution: f (x) = cos a x, If n = 1, a x dx = Pn=1 cos (n+1) a x sin n a x az a x(cid:12)(cid:12)(cid:12)(cid:12) (n + 1)(cid:0)( 1)n + 1(cid:1) + bn = az a b1 = The fourier sine series for f is therefore for 0 x < a. cos a x . Writing f (x) = cos a x, the coe cients bn in the fourier sine series are computed as follows: x + sin (n 1) a x(cid:1) dx a a. 0 if n is odd, n 3. sin a x cos a x dx = a. 1 a sin2 a x(cid:12)(cid:12)(cid:12)(cid:12) sin 2n a x. |x| > . (a) find the fourier integral of f. (b) for which values of x does the integral converge to f (x)? (c) evaluate the integral for < x < . 1 2 d f (x) =( cos x.
