Squeeze theorem for functions. Let A = (a, b) \\{c}, where a

Squeeze theorem for functions. Let A (a, b) \ {c}, where a < c < b. Then let f: A * R, g: A * R and h: A * R be functions such that f (x) S g(x) S h(x) for all x e A. Suppose that the functions f and h have a limit at the point c and limf(x) = limh(x). Prove that the function g has also a limit at the point c and it holds limg(x) = limf(x). x-*c