Problem 1. The following function has domain (-1, 0) U (0, co), f(x) = +V1+x Make a table of values of f(x) for x - +1, +0.1, +0.01, and #0.001. Use your table to guess a limiting value for f(x) as x -> 0. Finally, use difference- of-squares rationalization to find a continuous function g(x) whose domain contains (-1, co) such that f(x) equals g(x) on (-1, 0) U (0, co). Use this to prove that your guess is correct. Problem 2. Define a function h(x) on (-oo, too) by the following rule, h(z) = sin (1/x), x70 . 0 , * = 0 Compute the limit as x approaches 0 of k(x) = xh(x). Explain why it is invalid to simply compute the limit as k(0) = 0 . h(0) = 0 . 0 =0