Chapter 2.7, Problem 31E

Limit proofs Use the precise definition of a limit to prove the following limits. Specify a relationship between ε and δ that guarantees the limit exists.

  31.     $\underset{x\to -3}{\lim }\left|2x\right|=6$ (Hint: Use the inequality $\Vert a|-|b\Vert \le \left|a-b\right|$, which holds for all constants a and b (see Exercise 74).)