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Prove the following

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

$\lim _{x \rightarrow 3}(x+3)=6$

$\lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3}=6$

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