Infinite String: consider the initial/boundary value problem au = 2 ou at2 dx 2 ' xER, t> 0, u(x, 0) = f(x), xER du at (x, 0) = 8(x), xER where f and g are two given twice differentiable functions. We showed in class that this problem is solved by he d'Alembert's solution u(x, t) = =[f(x + ct) + f(x - ct) ]+, [G(x + ct) - G(x - where G is an antiderivative of g. Sketch the solution for t = 0, 1, 2, 3, where f(x) and g(x) are given below. a) f(x) = 10 1-x2 x| ] ' 8(x) = 0 b) f(x) =0 8(x) = 10 sin rx |x| 1