# $f(x) = [tan^2 x]$ where [.] denotes the greatest integer function. Then

Q: Let $f(x) = [tan^2 x]$ where [.] denotes the greatest integer function. Then

(A) $\lim_{h \rightarrow 0} f(x)$ does not exist

(B) f(x) is continuous at x = 0

(C) f(x) is not differentiable at x = 0

(D) f'(0) = 1

Sol: $\lim_{h \rightarrow 0} [tan^2 (0+h)] = \lim_{h \rightarrow 0} [tan^2 (0-h)]= [tan^2 (0)] = 0$

So, 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.