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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 $-3$.

 

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