3. 4. Given the following function f(x)=e¹, 0≤x≤ 2, f(x) = f(x+4). Sketch the graph of even periodic extension of f(x) o

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3 4 Given The Following Function F X E 0 X 2 F X F X 4 Sketch The Graph Of Even Periodic Extension Of F X O 1 (44.57 KiB) Viewed 13 times

3. 4. Given the following function f(x)=e¹, 0≤x≤ 2, f(x) = f(x+4). Sketch the graph of even periodic extension of f(x) over -4 ≤ x ≤ 4. Hence, find the Fourier cosine series expansion for f(x). By using separation of variables, show that the solution for the follow- ing heat equation with mixed boundary condition is given by ди 2²u Ət əx²¹ = u(0,t)=0, u(x,0) = 1, 0<x<1, t> 0, uz(1,t)=0, t>0, 0<x< 1, 4 (2n-1) T u(x, t) = [₁ n=1 sin (2n − 1)πx- (²-1²-²1 (2n-1)22t 2