Question

The value of $\underset{x\to 2}{\lim }\frac{e^{3x-6}-1}{\sin \left(2-x\right)}$ is

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

Answer 1

Answer: (C)

$\underset{x\to 2}{\lim }\frac{e^{3x-6}-1}{\sin \left(2-x\right)}$

$=\underset{x\to 2}{\lim }-\frac{e^{3x-6}\left(3\right)}{\cos \left(2-x\right)}$

(using L’Hospital’s rule)

$=-\frac{3e^0}{\cos 0}=-3$