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Infinite String: consider the initial/boundary value problem 62\": xER, t>0, 67 6x2, "(17,0) = f(x), x E R an 305, 0) _ g(X), x E R 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)] + 2ic[G(x + ct) G(x ct)], where G is an antiderivative of g. Sketch the solution fort = 0, 1, 2, 3, where f (x) and g(x) are given below. a) _ 1x2 |x|15 g(x)_0 b) f(x)=0 g(x)={f)m'\"' {3:}