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6. Let f be a 20-periodic function, such that f(x) = x2 on (-1, ). The...


6. Let f be a 20-periodic function, such that f(x) = x2 on (-1, ). The Fourier series of f is given by 72 (-1)cos(nx) n2 +4
(b) Determine for which values of x the following series converges and find the limit for all the values of x where the serie
6. Let f be a 20-periodic function, such that f(x) = x2 on (-1, ). The Fourier series of f is given by 72 (-1)"cos(nx) n2 +4 3 n=1 (a) Does the Fourier series of f converge pointwise to f on R? Is the convergence uniform?
(b) Determine for which values of x the following series converges and find the limit for all the values of x where the series converges: (-1)"sin(nx) n n=1 Does this series converge uniformly on R? (c) Find the value of n4 n=1
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6. Let f be a 20-periodic function, such that f(x) = x2 on (-1, ). The...
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