Question

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

• A. $\underset{x\to 0}{lim}f\left(x\right)$ does not exist
• B. $f\left(x\right)$ is continuous at $x=0$
• C. $f\left(x\right)$ is not differentiable at $x=0$
• D. $f\left(x\right)=1$

Answer 1

The correct option is B $f\left(x\right)$ is continuous at $x=0$

Given, $f\left(x\right)=\left[{\tan }^{2}x\right]$

Now, $\underset{x\to 0}{lim}f\left(x\right)=\underset{x\to 0}{lim}\left[{\tan }^{2}x\right]=0$

and $f\left(0\right)=\left[{\tan }^{2}0\right]=0$

Hence, $f\left(x\right)$ is continuous at $x=0$