Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • 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)

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

 

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

CBSE Central Sector Scheme of Scholarship 2025 applications open on scholarships.gov.in
anam-khan

CBSE Board 2025: Class 10th, 12th supplementary date sheet out; exams from July 15
anam-khan

CBSE issues final reminder to schools for supplementary exam LOC submission; submit by today without late fee

Latest Question