Chapter 2.5, Problem 15E

Suppose the function g satisfies the inequality $3-\frac{1}{x^2}\le g\left(x\right)\le 3+\frac{1}{x^2}$, for all nonzero values of x. Evaluate $\underset{x\to \infty }{\lim }g\left(x\right)$ and $\underset{x\to -\infty }{\lim }g\left(x\right)$.