Question

Evaluate :$\underset{x\to 0}{lim}x{\log }_e\left(\sin x\right)$ is equal to

• A. $-1$
• B. ${\log }_{e}1$
• C. $0$
• D. None of these.

Answer 1

The correct option is C $0$

$=\underset{x\to 0}{lim}\frac{ln\left(\sin x\right)}{\frac{1}{x}}=\underset{x\to 0}{lim}\frac{\frac{1}{\sin x}\cos x}{\frac{-1}{x^2}}=\underset{x\to 0}{lim}\frac{\cos x}{\sin x\times x}\times x\times x^2=0$