Chapter 2.7, Problem 32E

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.

32.     $\underset{x\to 25}{\lim }\sqrt{x}=5$ (Hint: The factorization $x-25=\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)$ implies that $\sqrt{x}-5=\frac{x-25}{\sqrt{x}+5}$.)