Problem 2. Suppose u solves the following initial value problem Utt Uxx = 0 ult=0 = 11-2,-1)(L) + 1[1,2] (2) ut|t=0 = 0 XER, t > 0, XER, XER, (3) where i 1 (-2, 1] 11-2,-1)(x) = and 10 otherwise Sketch the region on the st-plane where u(x, t) = 0. 1[1,2] (2) = i r [1,2] otherwise 0 Problem 2. Suppose u solves the following initial value problem Utt Uxx = 0 ult=0 = 11-2,-1)(L) + 1[1,2] (2) ut|t=0 = 0 XER, t > 0, XER, XER, (3) where i 1 (-2, 1] 11-2,-1)(x) = and 10 otherwise Sketch the region on the st-plane where u(x, t) = 0. 1[1,2] (2) = i r [1,2] otherwise 0