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

The correct option is C $0$

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

$=\underset{x\to 0}{lim}\frac{x{e}^x}{x}-\underset{x\to 0}{lim}\frac{\sin x}{x}$, split up

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

$=e^0-1=1-1=0$