Given f (x) =4,, - ,,{left( {frac{1}{2}, - ,x} right)^{2/3}}, g (x) = left{ begin{array}{l}frac{{tan

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5. Continuity and Differentiation

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Given $f (x) =4\,\, - \,\,{\left( {\frac{1}{2}\, - \,x} \right)^{2/3}}\,$ $g (x) = \left\{ \begin{array}{l}\frac{{\tan \,\,[x]}}{x}\,\,\,\,,\,\,x \ne \,0\\1\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,x\, = \,0\end{array} \right.$

$h (x) = \{x\}$ $k (x) = {5^{{{\log }_2}(x\, + \,3)}}$then in $[0, 1]$ Lagranges Mean Value Theorem is $NOT$ applicable to

A

$f, g, h$

B

$h, k$

C

$f, g$

D

$g, h, k$

Solution

$f$ is not differentiable at $x =\frac{1}{2} $

$g$ is not continuous in $[0, 1]$ at $x = 0$

$h$ is not continuous in $[0, 1]$ at $ x = 1$ & $0 $

$k (x) = {(x + 3)^{{{\ln }_2}5}}= (x + 3)^p$ where $2 < p < 3$

Standard 12

Mathematics

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(JEE MAIN-2021)