Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Very short answer type question 7

Need solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Very short answer type question  7

Answers (1)

Answer: 1

Hint: if f(x) is not differentiable then L H D \neq R H D

Given:f(x)=\left|\log _{e} x\right| is not differentiable.

Explanation: f(x)=\left|\log _{e} x\right|=\left\{\begin{array}{cc} \log _{e} x & x \geq 1 \\ -\log _{e} x & 0<x<1 \end{array}\right\}

as logarithmic function is differentiable in its domain. So we only have to check at x=1

        \begin{aligned} &L H D=\lim _{x \rightarrow 1^{-}} \frac{f(x)-f(1)}{x-1} \\\\ &=\lim _{x \rightarrow 1} \frac{-\log _{e} x-0}{x-1} \\\\ &=\lim _{x \rightarrow 1} \frac{-\log x}{x-1} \end{aligned}

applying  L' Hospital rule

        \begin{aligned} &=\lim _{x \rightarrow 1} \frac{-1}{x} \\ &=-1 \end{aligned}

        \begin{aligned} &R H D \text { atx }=1 \\\\ &\lim _{x \rightarrow 1^{+}} \frac{f(x)-f(1)}{x-1} \\\\ &\lim _{x \rightarrow 1^{+}} \frac{\log _{e} x-\log 1}{x-1} \end{aligned}

        \begin{aligned} &=\lim _{x \rightarrow 1} \frac{\log _{e} x-0}{x-1} \\\\ &=\lim _{x \rightarrow 1} \frac{\log x}{x-1} \end{aligned}

applying  L' Hospital rule

        \begin{aligned} &=\lim _{x \rightarrow 1} \frac{1}{x} \\\\ &=1 \\\\ &\text { As } L H D \neq R H D_{\text {at }} \mathrm{x}=1 \end{aligned}

\left|\log _{e} x\right| is not differentiable at x=1

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question