Solve the IBVP for heat equation. Also find the limit of u(x,t) as t -> inf ut = 3uxx + F(x,t),   0 < x < 1,    t > 0 u(0,t) = u(1,t) = 0,    t > 0 u(x,0) = sin(pi*x),    0 < x < 1,    t > 0 Where: F(x,t) = 4,   0 < x < 1/2 F(x,t) = 0,   1/2 < x < 1

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