MCQ
જો $f(x) = \left\{ \begin{array}{l}x\sin \frac{1}{x},\;\;\;\;\;x \ne 0\\\;\;\;\;\;\;0,\;\;\;\;\;x = 0\end{array} \right.$, તો $\mathop {\lim }\limits_{x \to 0} f(x) = $
- A$1$
- ✓$0$
- C$-1$
- Dએકપણ નહી.
Since $ - 1 \le \sin \frac{1}{x} \le 1\,\, \Rightarrow \,\, - |\,\,x\,\,|\,\, \le x\sin \frac{1}{x} \le \,\,|\,\,x\,\,|$
We know that $\mathop {\lim }\limits_{x \to 0} \,\,|\,\,x\,\,|\, = 0$ and $\mathop {\lim }\limits_{x \to 0} \,\,|\,\,x\,\,|\, = 0$
In this way $\mathop {\lim }\limits_{x \to 0} \,\,f(x) = 0.$
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