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 0, uz(1,t)=0, t>0, 0