Question:
Evaluate
$\lim _{x \rightarrow 3}\left(\frac{x^{2}-4 x}{x-2}\right)$
Solution:
To evaluate:
$\lim _{x \rightarrow 3} \frac{x^{2}-4 x}{x-2}$
Formula used: We have,
$\lim _{x \rightarrow a} f(x)=f(a)$
As $\mathrm{x} \rightarrow 3$, we have
$\lim _{x \rightarrow 3} \frac{x^{2}-4 x}{x-2}=\frac{3^{2}-4(3)}{3-2}$
$\lim _{x \rightarrow 3} \frac{x^{2}-4 x}{x-2}=\frac{3^{2}-4(3)}{3-2}$
$\lim _{x \rightarrow 3} \frac{x^{2}-4 x}{x-2}=-3$
Thus, the value of $\lim _{x \rightarrow 3} \frac{x^{2}-4 x}{x-2}$ is $-3$.