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  • Provide solution for rd sharma maths class 12 chapter 9 Differentiability exercise Multiple choice question, question 8

Provide solution for rd sharma maths class 12 chapter 9 Differentiability exercise Multiple choice question, question 8

Answers (1)

(b)

HINTS: Understand the  definition of continuity and differentiability

GIVEN: f(x)=\sqrt{1-\sqrt{1-x^{2}}}

SOLUTION:The function is defined only when

\begin{aligned} &1-x^{2}>0 \\ &1>x^{2} \\ &-1<x<1 \end{aligned}

Now between x \in[-1,1] at  x=0

f(x)=0

So we Check the continuity at x=0

LHD =

\begin{aligned} \lim _{x \rightarrow 0^{-}} f(x) &=\lim _{x \rightarrow 0} \sqrt{1-\sqrt{1-x^{2}}} \\ &=0 \end{aligned}

RHD  =

\begin{aligned} \lim _{x \rightarrow 0^{+}} f(x) &=\lim _{x \rightarrow 0} \sqrt{1-\sqrt{1-x^{2}}} \\ &=0 \end{aligned}

As LHD = RHD

M(-1,1)

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