Exercise 1: Suppose lim f(x)= xC = L, lim g(x) xC - M and there exists a positive number 8 such that f(x) g(x) Vx (c-d,c + 8)\{c}. Prove that L > M. Give an example such that f(x) > g(x) \x R but lim f(x) and lim g(x) both exist and are equal. X-C x-C Exercise 2: Suppose lim f(x) = 0 and there exists positive numbers p and M such that x-C g(x) M Vx (c-p,c + p)\{c}. _sin Prove that lim f(x)g(x) = 0. Use this result to show that lim tan(x) es xC = 0