Question

Let [.] denotes greatest integer function and f(x) = [tan²x] 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

Answer 1

Answer: (B)

f(x) is continuous at x = 0

Answer 2

0 £ tan²x < 1, – $\frac{\pi}{4}$ < x < $\frac{\pi}{4}$

̃ [tan²x] = 0, – $\frac{\pi}{4}$ < x < $\frac{\pi}{4}$

\ f is continuous and derivable in $\left( - \frac{\pi}{4},\frac{\pi}{4} \right)$