MCQ
જો $f(x) = \left\{ \begin{array}{l}x,\;\;{\rm{if\, }}x\,{\rm{ \,is \,rational\, }}\\ - x,\;{\rm{if \,\,}}x\,{\rm{\, is\, irrational\,}}\end{array} \right.,$ તો $\mathop {\lim }\limits_{x \to 0} f(x) = . . .$
- ✓$0$
- B$1$
- C$ -1$
- Dમેળવી શકાય નહી.
and $\mathop {\lim }\limits_{x \to {0^ + }} f(x) = \mathop {\lim }\limits_{h \to 0} f(0 + h) = \mathop {\lim }\limits_{h \to 0} \,\,\, - (0 + h) = 0$
$\therefore \,\,\,\mathop {\lim }\limits_{x \to 0} \,\,f(x) = 0$, $\left( {\because \mathop {\lim }\limits_{x \to {0^ - }} f(x) = \mathop {\lim }\limits_{x \to {0^ + }} f(x)} \right)$ .
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