question_answer 1)

Discuss the continuity of the following functions : (a) f (x) sin x + cos x (b) f(x) =sin x – cos x (c) f(x) = sin x . cos x  

Answer:

(a) Let f(x) = g(x) + h(x) g(x) = sin x and h(x) = cos x. Since sine and cosine functions are everywhere continuous. Therefore f(x) = g(x) + h (x) is also continuous Sum of continuous functions also continuous) (b) Being difference of continuous functions [(sine and cosine functions are every where continuous] f is continuous. (c) Being product of continuous function (sine and cosine are everywhere continuous). f is continuous function.