Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • I need help with - Limit , continuity and differentiability - JEE Main-14

If  f(x)=[x]-\left [ \frac{x}{4}\right ],x\:\:\varepsilon \:\:Rwhere  [x]  denotes   the greatest integer function , then :

  • Option 1)

    f is continuous at x=4.

  • Option 2)

    \lim_{x\rightarrow 4+}f(x)  exist but    \lim_{x\rightarrow 4-}f(x) does not exist.

  • Option 3)

    Both  \lim_{x\rightarrow 4-}f(x)  and \lim_{x\rightarrow 4+}f(x)   exist but are not equal .

  • Option 4)

      \lim_{x\rightarrow 4-}f(x)  exist but \lim_{x\rightarrow 4+}f(x)  does not exist .

 

Answers (1)

best_answer

f(x)=[x]-\left [ \frac{x}{4}\right ],x\:\:\varepsilon \:\:R

\\ \lim_{h\rightarrow o^{+}}\left [ 4+h \right ]-\left [ \frac{4+h}{4} \right ]\\\\\:=4-1=3

\\ \lim_{h\rightarrow o^{-}}\left [ 4-h \right ]-\left [ \frac{4-h}{4} \right ]\\\\\:=3-0=3

\lim_{h\rightarrow o^{+}}=\lim_{h\rightarrow o^{-}}

hence f(x)  is continous at  x=4

 


Option 1)

f is continuous at x=4.

Option 2)

\lim_{x\rightarrow 4+}f(x)  exist but    \lim_{x\rightarrow 4-}f(x) does not exist.

Option 3)

Both  \lim_{x\rightarrow 4-}f(x)  and \lim_{x\rightarrow 4+}f(x)   exist but are not equal .

Option 4)

  \lim_{x\rightarrow 4-}f(x)  exist but \lim_{x\rightarrow 4+}f(x)  does not exist .

Posted by

solutionqc

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions
anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in
anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question