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  • Explain solution rd sharma class 12 chapter 9 Differentiability exercise Multiple choice question, question 22

Explain solution rd sharma class 12 chapter 9 Differentiability exercise Multiple choice question, question 22

Answers (1)

(d)

HINTS: check at x=3 LHL & RHL,LHD & RHD

GIVEN: f(x)=|3-x|+(3+x)

SOLUTION:

To check at x=3 we take the interval [2,4]

\begin{aligned} f(x) &= \begin{cases}3-x+(3+3) & 2<x<3 \\ -3+x+3+4 & 3<x<4\end{cases} \\ &= \begin{cases}-x+9 & 2<x<3 \\ x+4 & 3<x<4\end{cases} \end{aligned}

As (x) divides the least integer function.

At x=3

\begin{aligned} &\lim _{x \rightarrow 3^{-}} f(x)=\lim _{h \rightarrow 0}-x+9=-3+9=6 \\ &\lim _{x \rightarrow 3^{-}} f(x)=\lim _{h \rightarrow 0}-x+4=3+4=7 \end{aligned}

As LHL \neq RHL

So f(x) is not continuous at x=3

So f(x) is also  not differentiable at x=3

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