Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

If \mathrm{f(x)=\sum_{n=0}^n a_n|x|^n,}  where \mathrm{a_i 's} are real constants, then \mathrm{f(x)}  is
 

Option: 1

 continuous at \mathrm{x=0} for all \mathrm{a_i}
 


Option: 2

 differentiable at \mathrm{x=0}  for all \mathrm{a_i \in R} 
 


Option: 3

 differentiable at \mathrm{x=0} for all \mathrm{a_{2 k+1}=0}
 


Option: 4

 none of these


Answers (1)

best_answer

\mathrm{|x|,|x|^2}, etc., are all continuous everywhere and the algebraic sum of continuous functions is also continuous. So, (a) is correct. \mathrm{|x|,|x|^3}, etc., are not differentiable at \mathrm{ x=0}, whereas \mathrm{|x|^2,|x|^4}, etc, are all differentiable at \mathrm{x=0}.

Hence, (c) is correct.

Posted by

sudhir kumar

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

JEE Main 2026 session 2 application correction begins on jeemain.nta.nic.in; edit details by tomorrow
anam-khan

JEE Main 2026 Registration LIVE: Session 2 exam from April 2 to 9; shift timings, admit card, exam pattern
anam-khan

JEE Main 2026 session 2 registration ends today for BTech, BArch; apply at jeemain.nta.nic.in

Latest Question