Let f(x) = [tan2x], where [.] denotes the greatest integer function. Then
Answer & explanation
Correct answer: option 2
$\underset{h→0}{\lim}[tan^2(0+h)]=\underset{h→0}{\lim}[tan^2(0-h)]=[tan^20]=0$
⇒ f(x) is continuous at x = 0.
Since f(x) = 0 in the neighbourhood of 0, f'(0) = 0.
Hence (B) is the correct answer.