Question

Let f(x) = [tan²x], where [.] denotes the greatest integer function. Then

• A. $\frac{1}{3}$f(x) doesn’t exist
• B. f(x) is continuous at x = 0
• C. f(x) is not differentiable at x = 0
• D. f′(0) = 1

Answer 1

Answer: (B)

f(x) is continuous at x = 0

Answer 2

$\lim _ { h \rightarrow o }$ [tan²(0 + h)] = $\lim _ { h \rightarrow o }$ [tan²(0 – h)] = [tan²0] = 0

⇒ f(x) is continuous at x = 0.

Since f(x) = 0 in the neighbourhood of 0, f′(0) = 0