Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let denote the greatest integer function and <img alt="\mathrm{f(x)=\left[\tan ^{2} x\right]}" src="https:/

Let [\cdot] denote the greatest integer function and \mathrm{f(x)=\left[\tan ^{2} x\right]}. Then

Option: 1

\lim _{x \rightarrow 0} f(x) does not exist


Option: 2

f(x) is continuous at x=0


Option: 3

f(x) is not differentiable at x=0


Option: 4

f^{\prime}(0)=1.


Answers (1)

best_answer

For 0<x<\pi / 4,0<\tan ^{2} x<1 \Rightarrow\left[\tan ^{2} x\right]$ $=0$ for $0<x<\pi / 4$. As $\tan ^{2} x.  is an even function, so \mathrm{\lim _{x \rightarrow 0+} f(x)=\lim _{x \rightarrow 0+} f(x)=0}. So \mathrm{f} is continuous at \mathrm{x=0}.


Now \mathrm{\lim _{h \rightarrow 0} \frac{f(0+h)-f(0)}{h}=\lim _{h \rightarrow 0} \frac{f(h)-(0)}{h}=\lim _{h \rightarrow 0} \frac{0}{h}=0}.

Hence \mathrm{f} is differentiable at \mathrm{x=0} and  \mathrm{f^{\prime}(0)=0}.

Posted by

Ritika Harsh

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 Marks vs Percentile 2025: How many marks do you need to score 95+ percentile?
anam-khan

JEE Main 2025 session 1 official answer key out; challenge by February 6; how to calculate NTA score?
anam-khan

JEE Main 2025: NIT Raipur's CSE cut-offs drop; closing ranks in popular branches

Latest Question