Chapter 2.7, Problem 35E

Challenging limit proofs Use the definition of a limit to prove the following results.

35. $\underset{x\to 3}{\lim }\frac{1}{x}=\frac{1}{3}$ (Hint: As x → 3, eventually the distance between x and 3 is less than 1. Start by assuming |x – 3| < 1 and show $\frac{1}{\left|x\right|}<\frac{1}{2}$.)