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  • Explain solution RD Sharma class 12 chapter 9 Differentiability exercise Fill in the blanks question 16 maths

Explain solution RD Sharma class 12 chapter 9 Differentiability exercise Fill in the blanks question  16 maths

Answers (1)

best_answer

Answer: x=1

Given: The greatest integer function, f(x)=[x], 0<x<2

Solution:

RHD:

f(x)=x

\begin{aligned} R f^{\prime}(0) &=\lim _{h \rightarrow 0} \frac{f(1+h)-f(1)}{h} \\\\ &=\lim _{h \rightarrow 0} \frac{[1+h]-[1]}{h} \\\\ &=\lim _{h \rightarrow 0} \frac{(1-1)}{h} \\\\ &=0 \end{aligned}

LHD

    \begin{aligned} &L f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{f(1-h)-f(1)}{-h} \\\\ \end{aligned}

                 \begin{aligned} &=\lim _{h \rightarrow 0^{+}} \frac{[1-h]-[1]}{-h} \\\\ &=\lim _{h \rightarrow 0^{+}} \frac{0-1}{-h} \\\\ &=\lim _{h \rightarrow 0} \frac{1}{h} \\\\ &=\infty \end{aligned}

Since RHD \neq LHD

\therefore f(x) is not differentiable at x=1

 

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