Infinite String: consider the initial/boundary value problem x E R, t > 0, dx2 f(x), и(х, 0) x E R ди (x, 0) = g(x), dt x E R where f and g are two given twice differentiable functions. We showed in...

Extracted text: Infinite String: consider the initial/boundary value problem x E R, t > 0, dx2 f(x), и(х, 0) x E R ди (x, 0) = g(x), dt 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) = LS(x + ct) - ct) + f(x – ct)] + 2c IG(x + ct) – G(x – ct)], 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) [1 – x² |x| < 1="" |x|=""> 1 ' f(x) = g(x) = 0 b) sin Tx f(x) = 0 g(x) ={ |x| < 1="" i지=""> 1