Question

Let [.] denotes the greatest integer function and f(x)= [tan² x], then

(a) lim f(x) (for x → 0) does not exist

(b) f (x) is continuous at x = 0

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

(d) f '(0) = 1

Answer 1

Correct option (b) f (x) is continuous at x = 0

Explanation :

i.e, f(x) is zero for all values of x from x = - 45° to 45°.

Thus, f(x) exists when x → 0 and also it is continuous at x = 0.

Also, f(x) is differentiable at x = 0 and has a value of zero.