Question

Which of the following is true about f(x)=sinx+cosx?

(a) Continuous everywhere

(b) Continuous at x=\(\frac{\pm n\pi}{2}\), where n is any integer

(c) Continuous at x=\(\frac{\pm (n+1)\pi}{2}\), where n is any integer

(d) Continuous at x=0

I have been asked this question in an international level competition.

The above asked question is from Continuity topic in chapter Complex Function Theory of Engineering Mathematics

Answer 1

The correct answer is (a) Continuous everywhere

Best explanation: The values of sinx and cosx never become infinity or non-determinable for any value of x. Therefore, the function f(x)=sinx+cosx is continuous at all points of x.