1. Let's recall the Pinching (Squeeze) theorem (Theorem 2.5.1): Suppose there are three functions f, g, and h that satisfy the following inequalities on a given interval containing a constant c. h(x) 0 If the functions h and g have the same limits as x approaches c, then the function f also has the same limit. That is, if lim h(x) = lim g(x) = L, for some real number L, then lim f (x) = L. Now, our goal is to generalize this theorem. The following is our initial incorrect attempt. You are going to fix it. Suppose there are three functions f, g, and h that satisfy the following inequalities h(x) 0 and lim h(x) = H, lim f(x) = F, and lim g(x) = G, for some real numbers H, F, and G. I-C We claim that H