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Need solution for rd sharma maths class 12 chapter 9 Differentiability exercise Multiple choice question, question 20

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Hint: understand the greatest integer function

Given : f(x)=\frac{\sin (\pi[x-\pi])}{h+[x]^{2}} \cdots(i)

Explanation : \pi[x-\pi]=n \pi

Taking sin on both sides

\begin{aligned} &\sin (\pi[x-\pi])=\sin (n \pi) \\ &\sin (\pi[x-\pi])=0 \end{aligned}

Put in 0

\begin{aligned} f(x) &=\frac{0}{h+[x]^{2}} \quad\left[a s h+[x]^{2} \neq 0\right] \\ &=0 \end{aligned}

As f(x) is constant function so it is continuous as well as differentiable for all x \in R

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