माना $f(x) = \left\{ \begin{array}{l}1\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\forall x < 0\\1 + \sin x,\,\,\,\forall 0 \le x \le \pi /2\end{array} \right.,$ तब $f'(x)$ का $x = 0$ पर मान है
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Answer
$f(x) = \left\{ \begin{array}{l}\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\forall x < 0\\1 + \sin x,\,\,\,\forall \,0 \le x < \frac{\pi }{2}\end{array} \right.$
$\therefore \,\,f'(x) = \left\{ \begin{array}{l}\,\,\,0,\,\,\,\,\forall \,x < 0\,({\rm{LHD}})\\\cos x,\,\,0 \le x \le \pi /2,\,\,({\rm{RHD}})\end{array} \right.$
$\therefore \,f'(0) = \left\{ \begin{array}{l}\,\,0\,\,\,\,,\,\,x < 0\\\cos 0 = 1\end{array} \right.$,
$\therefore \,f'(0)$अस्तित्व नहीं है।
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