Question

If$f(x) = \left\{ \begin{aligned} & \begin{matrix} x\sin\frac{1}{x}, & x \neq 0 \end{matrix} \\ & \begin{matrix} 0, & x = 0 \end{matrix} \end{aligned} \right.\$, then $\lim_{x \rightarrow 0}f(x)$ =

• A. 1
• B. 0
• C. –1
• D. None of these

Answer 1

Answer: (B)

0

Answer 2

$\lim_{x \rightarrow 0}x\sin\left( \frac{1}{x} \right) = \left( \lim_{x \rightarrow 0}x \right)\left( \lim_{x \rightarrow 0}\sin\frac{1}{x} \right)$ = 0

× (A number oscillating between – 1 and 1) = 0.