Let fn(x) : on [0, 1]. 1+ x" (a) Prove that fn converges uniformly to 0 on [0, e], Ve E (0, 1). (b) Does fn converge uniformly on [0, 1]? Prove or disprove. x sin nx Let fn(x) = x + on R. n (a) Prove...

0. (b) Does fn converge uniformly on R? Prove or disprove. "/>
Extracted text: Let fn(x) : on [0, 1]. 1+ x" (a) Prove that fn converges uniformly to 0 on [0, e], Ve E (0, 1). (b) Does fn converge uniformly on [0, 1]? Prove or disprove. x sin nx Let fn(x) = x + on R. n (a) Prove that fn converges uniformly to x on [-R, R], VR > 0. (b) Does fn converge uniformly on R? Prove or disprove.