3. Recall that a Fourier series will converge quickly if the periodic extension of the function is continuous and slowly if it is discontinuous. If the Fourier series converges quickly, we say that it "converges uniformly". Sketch the periodic extensions of the following functions and determine from the continuity whether the Fourier series converges uniformly or not. (Hint: there is no need to calculate any Fourier coefficients.) (a) The periodic extension of f (x) = 1 – x² over the interval [-1, 1] (b) The periodic extension of f(x) = sin(Tx) over the interval [-1/2, 1/2]

3. Recall that a Fourier series will converge quickly if the periodic extension of the function is continuous and slowly if it is discontinuous. If the Fourier series converges quickly, we say that it "converges uniformly". Sketch the periodic extensions of the following functions and determine from the continuity whether the Fourier series converges uniformly or not. (Hint: there is no need to calculate any Fourier coefficients.) (a) The periodic extension of f (x) = 1 – x² over the interval [-1, 1] (b) The periodic extension of f(x) = sin(Tx) over the interval [-1/2, 1/2]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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