Question

Which of the following is true about f(x)=tanx?

(a) Continuous at x=$\frac{\pi}{2}$

(b) Continuous at x=$-\frac{3\pi}{2}$

(c) Continuous at x=0

(d) Continuous at x=$\frac{3\pi}{2}$

This question was addressed to me in homework.

I'm obligated to ask this question of Continuity in section Complex Function Theory of Engineering Mathematics

Answer 1

Correct choice is (c) Continuous at x=0

Explanation: tanx=$\frac{sinx}{cosx}$

cosx=0 when x=$\frac{\pm (n+1)\pi}{2}$ which are points of discontinuity for the function, f(x)=tanx.