Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Consider <img alt="\mathrm{f(x)=\left[\frac{2\left(\sin x-\sin ^3 x\right)+\left|\sin x-\sin ^3 x\right|}{2\left(\sin x-\sin ^3 x\right)-\left|\sin x-\sin ^3 x\right|}\right], x \neq \pi / 2 for x

Consider \mathrm{f(x)=\left[\frac{2\left(\sin x-\sin ^3 x\right)+\left|\sin x-\sin ^3 x\right|}{2\left(\sin x-\sin ^3 x\right)-\left|\sin x-\sin ^3 x\right|}\right], x \neq \pi / 2 for x \in(0, \pi)} and \mathrm{f(\pi / 2)=3}, Where [ ] denotes the greatest integer function, then

Option: 1

f is continuous and differentiable at x=\pi / 2


Option: 2

f is continuous but not differentiable at x=\pi / 2
 


Option: 3

f is neither continuous nor differentiable at x=\pi / 2


Option: 4

none of these.


Answers (1)

best_answer

\mathrm{\text { Given } f(x)=\left[\frac{2 \sin x(1-\sin x)(1+\sin x)+|\sin x||1-\sin x||1+\sin x|}{2 \sin x(1-\sin x)(1+\sin x)-|\sin x||1-\sin x||1+\sin x|}\right]}

\mathrm{ =\left[\frac{3}{1}\right]=3 \text { for } x \in(0, \pi) ; x \neq \pi / 2 }

Also \mathrm{f(\pi / 2)=3 (given)}

\Rightarrow f is continuous at  and also differentiable at x=\pi / 2 (as f is a constant function).

Posted by

qnaprep

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 2025: NIT Rourkela cut-offs for CSE, chemical engineering drop; last years' closing ranks
anam-khan

JEE Main 2025 Live: NTA exam city slip at jeemain.nta.nic.in soon; session 1 schedule
anam-khan

JEE Main 2025 schedule out for session 1; paper 1 from January 22

Latest Question