Question:
Evaluate
$\lim _{x \rightarrow 3}\left(\frac{x^{2}+9}{x+3}\right)$
Solution:
To evaluate:
$\lim _{x \rightarrow 3} \frac{x^{2}+9}{x+3}$
Formula used:
We have,
$\lim _{x \rightarrow a} f(x)=f(a)$
As $x \rightarrow 3$, we have
$\lim _{x \rightarrow 3} \frac{x^{2}+9}{x+3}=\frac{3^{2}+9}{3+3}$
$\lim _{x \rightarrow 3} \frac{x^{2}+9}{x+3}=\frac{18}{6}$
$\lim _{x \rightarrow 3} \frac{x^{2}+9}{x+3}=3$
Thus, the value of $\lim _{x \rightarrow 3} \frac{x^{2}+9}{x+3}$ is $3 .$
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