Question

If $f\left(x\right)=x\sin \left(1/x\right),x\ne 0$, then ${lim}_{x\to 0}f\left(x\right)=$

• A. $1$
• B. $0$
• C. $-1$
• D. $doesnotexists$

Answer 1

Answer: (B)

$0$

Solution-

$f\left(x\right)=xsin\left(\frac{1}{x}\right),x\ne 0.$

$\underset{x\to 0}{lim}f\left(x\right)$

$sin\left(\frac{1}{x}\right)$ at x = 0 gives value between -1 & 1

OX (Arg value between -1 & 1) = $\underset{x\to 0}{lim}f\left(x\right)$

$=0$

B is correct.