Question

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

• A. $\frac{3}{5}$
• B. $\frac{1}{5}$
• C. $\frac{2}{7}$
• D. $\frac{1}{7}$

Answer 1

Answer: (D)

We have, $\underset{x\to 2}{\lim }\left(\frac{x-2}{x^3-x^2-x-2}\right)$
$=\underset{x\to 2}{\lim }\left(\frac{x-2}{\left(x-2\right)\left(x^2+x+1\right)}\right)$
$=\underset{x\to 2}{\lim }\left(\frac{1}{x^2+x+1}\right)$
$=\frac{1}{4+2+1}=\frac{1}{7}$