Question

The value of $\underset{x\to 2}{\lim }\left(\frac{1}{x-2}-\frac{4}{x^3-2x^2}\right)$ is

Answer 1

$\underset{x\to 2}{\lim }\left(\frac{1}{x-2}-\frac{4}{x^3-2x^2}\right)=\underset{x\to 2}{\lim }\left(\frac{1}{x-2}-\frac{4}{x^2\left(x-2\right)}\right)=\underset{x\to 2}{\lim }\left(\frac{x^2-4}{x^2\left(x-2\right)}\right)=\underset{x\to 2}{\lim }\left(\frac{\left(x-2\right)\left(x+2\right)}{x^2\left(x-2\right)}\right)=\underset{x\to 2}{\lim }\left(\frac{x+2}{x^2}\right)=\frac{2+2}{4}=1$