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 8 Continuity exercise Fill in the blanks question 11

need solution for RD Sharma maths class 12 chapter 8 Continuity exercise Fill in the blanks question 11

Answers (1)

Answer: All integral points

Hint: \left [ x \right ] is called greatest integer function

Given:  f(x)=x-\left [ x \right ] is discontinuous

Solution:

            Let c be an integer and g(x)=x-[x]

            g(x) is continuous at x=c ,if LHL=RHL=g(c)

            \begin{aligned} &\Rightarrow \lim _{x \rightarrow c^{-}} g(x)=\lim _{x \rightarrow c^{+}} g(x)=g(c)\\ &\text { LHL, }\\ &\lim _{x \rightarrow c^{-}} g(x)=\lim _{h \rightarrow 0} g(c-h) \end{aligned}

            \begin{aligned} &=\lim _{h \rightarrow 0} c-h-[c-1] \\ &=\lim _{h \rightarrow 0}(c-h)-[c-1] \\ &=\lim _{h \rightarrow 0}-h+1 \\ &=-0+1 \\ &=1 \end{aligned}

            \begin{aligned} &\mathrm{RHL}, \\ &\lim _{x \rightarrow c^{+}} g(x)=\lim _{h \rightarrow 0} g(c+h) \\ &=\lim _{h \rightarrow 0} c+h-[c+2h] \\ &=\lim _{h \rightarrow 0} c-h-c \\ &=\lim _{h \rightarrow 0}-h \\ &=0 \end{aligned}

            LHL\neq RHL

            Therefore, g(x) is not continuous.

            

              

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