Question

Let [ \text{ } ] denote the greatest integer function and f(x) = [tan^{2}x]. 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¢(0) = 1

Answer 1

Answer: (B)

f(x) is continuous at x = 0

Answer 2

f(x) = [tan²x] = 0 for –p/4 < x < p/4. Thus $\lim_{x \rightarrow 0}$f(x) exists and the value is 0. Moreover, it

is continuous at x = 0. Being a constant function f is differentiable at x = 0 and f¢(0) = 0