Q. Let [ ] denotes the greatest integer function and$f(x) = \lbrack\tan^{2}x\rbrack$. Then,
A) $\lim_{x \rightarrow 0}{f(x)}$ does not exist
B) $f(x)$ is continuous at $x = 0$
C) $f(x)$ is not differentiable at $x = 0$
D) $f(x) = 1$
Explanation
(b)
Given, $f(x) = \lbrack\tan^{2}x\rbrack$
Now, $\lim_{x \rightarrow 0}{f(x)} = \lim_{x \rightarrow 0}{\left\lbrack \tan^{2}x \right\rbrack = 0}$
And $f(0) = \left\lbrack \tan^{2}0 \right\rbrack = 0$
Hence, $f(x)$ is continuous at $x = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.