Chapter 13, Problem 2RCC

To evaluate the limit of a function, we often need to first rewrite the function using the rules of algebra. What is the logical first step in evaluating each of the following limits?

1. (a) $\underset{x\to 2}{\lim }\frac{x^2-4}{x-2}$
2. (b) $\underset{h\to 0}{\lim }\frac{{(5+h)}^2-25}{h}$
3. (c) $\underset{x\to 3}{\lim }\frac{\sqrt{x+1}-2}{x-3}$
4. (d) $\underset{x\to 7}{\lim }\frac{\left(\frac{1}{7}-\frac{1}{x}\right)}{x-7}$