Question:
1. $\lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3}$
Solution:
1. $\lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3}$
Given $\lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3}$
The above equation can be written as
$=\lim _{x \rightarrow 3} \frac{(x-3)(x+3)}{x-3}$
On simplifying and applying limits we get
$\lim _{x \rightarrow 3}(x+3)=6$
$\lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3}=6$