Chapter 1.6, Problem 51ES

Sketch the graphs of the curves $y=1/x,y=-1/x,$ and $y=f\left(x\right),$ where $f$ is a function that satisfies the inequalities $-\frac{1}{x}\le f\left(x\right)\le \frac{1}{x}$ for all $x$ in the interval $\left[1,+\infty \right)$ . What can you say about the limit of $f\left(x\right)$ as $x\to +\infty$ ? Explain your reasoning.