Question

$\underset{x\to \infty }{\lim }xSin\left(\frac{2}{x}\right)$ is equal to

• A. $\infty$
• B. 0
• C. $2$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$\underset{x\to \infty }{\lim }x\sin \left(\frac{2}{x}\right)=\underset{\frac{1}{x}\to 0}{\lim }\frac{\sin \left(\frac{2}{x}\right)}{\frac{1}{2}\left(\frac{2}{x}\right)}=2$