Answer
See explanations.
Work Step by Step
Step 1. To prove the limit $\lim_{x\to0}\frac{1}{|x|}=\infty$, for any large positive number $B$, we need to find a corresponding value $\delta\gt0$ so that for all x in the interval $0\lt|x|\lt\delta$, we get $\frac{1}{|x|}\gt B$
Step 2. The last inequality gives $|x|\lt 1/B$ ; thus we can choose $\delta=1/ B$ and when we go back in the steps, for all x in the interval $0\lt|x|\lt\delta$, we get $\frac{1}{|x|}\gt B$ which proves the limit statement.
