Question

$\underset{x\to 0}{\lim }\frac{x{e}^x-\sin x}{x}$ is equal to

• A. 3
• B. 1
• C. 0
• D. 2

Answer 1

Answer: (C)

$\underset{x\to 0}{\lim }\frac{x{e}^x-\sin x}{x}\left(\frac{0}{0}\text{form}\right)$
$=\underset{x\to 0}{\lim }\frac{x{e}^x+e^x-\cos x}{1}$ [using L' Hospital's rule]
$=0+1-1=0$