Question

$\underset{x\to 0}{lim}\left(\frac{e^x-e^{\sin x}}{x-\sin x}\right)=$

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

Answer: (C)

$1$

$\underset{x\to 0}{lim}\left(\frac{e^x-e^{\sin x}}{x-\sin x}\right)=\underset{x\to 0}{lim}{e}^{\sin x}\left(\frac{e^{x-\sin x}-1}{x-\sin x}\right)=e^0\cdot \log e=1$