13. At x = 28, the Fourier sine series of f (x) = x2 on [0, 3] converges to (a) o (b) 1 (c) 4 (d) -4 (e) None of these 14. The Fourier cosine series of f(x) = x on [0, 1] is a 2[(-1)" - 1] + n 27 2 COS(nTx) (b) 1 + 2[(-1)2 - 1] COS (nTx) n=1 n2 7 2 n=1 (c) 2[1 - (-1)22 OO + COS(nTx) (d) 1 - (-1) n272 2 cos (n7x) n=1 n272 n=1 (e) None of these 15. The solution of the heat equation ucr = gut, 0 0, which satisfies the boundary conditions u(0, t) = u(2, t) = 0 and the initial condition u(x, 0) = 2x, is u(x, t) = > bn sin nTX e - 9n2 72 t n=1 where on = (a) 8(-1)n 8(-1)n+1 (b) (c) 4(-1)n (d) 4(-1)n+1 nTT (e) None of these nT nTT nTT