1. Prove the following, using the definition of a one-sided limit. sin'x + 1 (a) lim x sin(Vx) = 0 2x (b) lim = 00 (c) lim = 0 r-0+ x2 - 4 r-1+x-1 4. Let f and g be functions defined on the open interval (a, b). Assume that L and M are real numbers so that lim f(x) = L and lim g(x) = M. Prove that the following -at r-at statements are true. (a) lim [f(x) + g(x)] exists, and lim If(x) + g(x)] = L + M. r-at r-at