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.