1 Consider the following IBVP for the heat equation on the line Ut 502x u x 0 f x where f x 0 x t 0 1 for 2 3 for 3 x 4 for x 4 a Find the solution and express it in terms of error functions b Sketch the graph of u x t when t 0 t 0 01 and t 0 1 c Using the formula that you found in part a check that lim u 3 5 t f 3 5 showing all work 0