Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Solve! - Limit , continuity and differentiability - JEE Main-10

Let f(x) = \sin |x|+ |x|   \forall x\epsilon R  then at x= 0 , f(x) is 

  • Option 1)

    continous and diffrentiable both

  • Option 2)

    continous but non diffrentiable 

  • Option 3)

    neither continous nor diffrentiable 

  • Option 4)

    discontinous but diffrentiable 

 

Answers (1)

best_answer

 As we have learned

Condition for differentiable -

A function  f(x) is said to be differentiable at  x=x_{\circ }  if   Rf'(x_{\circ })\:\:and\:\:Lf'(x_{\circ })   both exist and are equal otherwise non differentiable

-

 

 For continuity 

\lim_{x\rightarrow 0^{-}} \sin |x | + |x| = \lim_{x\rightarrow 0^{+}} \sin |x | + |x| = f(0)=0

\therefore f(x) is continous at x= 0

For diffrentiability 

LHD = \lim_{h\rightarrow 0^{+}}\frac{f(0-h)-f(0)}{(0-h)-(0)}=\lim_{h\rightarrow 0^{+}}\frac{\sin |h|+ |h|-0}{-h }

\lim_{h\rightarrow 0^{+}}\frac{\sin h+ h-0}{-h }=-1-1=-2

RHD = \lim_{h\rightarrow 0^{+}}\frac{f(0+h)-f(0)}{(h)}=\lim_{h\rightarrow 0^{+}}\frac{\sin |h|+ |h|-0}{h}

 \lim_{h\rightarrow 0^{+}}\frac{\sin h+ h-0}{h }=1+1=2

LHD\neqRHD 

so non diffrentiable at x= 0

 

 

 

 

 

 


Option 1)

continous and diffrentiable both

Option 2)

continous but non diffrentiable 

Option 3)

neither continous nor diffrentiable 

Option 4)

discontinous but diffrentiable 

Posted by

Himanshu

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