t→∞ 4. Let f(x) be a function defined for 0 ≤ x ≤ π with Π and f(x)dx = Π 2 Π f(x) cos(nx) dx = 2- (1-(-1)+1) πλη4 Write the Fourier Cosine Series for f(x) on [0,π]. b. Use a Fourier Cosine Series to find the solution to ( uε (x, t) = 1 uxx(x,t), 0 0, ux(0,t) = ux(n,t) = 0, u(x, 0) = f(x), t > 0, 0 < x <π. C. Give lim u(x, t). t→∞

t→∞ 4. Let f(x) be a function defined for 0 ≤ x ≤ π with Π and f(x)dx = Π 2 Π f(x) cos(nx) dx = 2- (1-(-1)+1) πλη4 Write the Fourier Cosine Series for f(x) on [0,π]. b. Use a Fourier Cosine Series to find the solution to ( uε (x, t) = 1 uxx(x,t), 0 0, ux(0,t) = ux(n,t) = 0, u(x, 0) = f(x), t > 0, 0 < x <π. C. Give lim u(x, t). t→∞

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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