Question

21. Discuss the continuity of the following functions:
(a) f(x) = sin x + cos x (b) f(x) = sin x-cosx
(c) f(x) = sin r. cos x​

Answer 1

Answer:

(a) f(x)=sinx+cosx

Let p(x)=sinx & q(x)=cosx

We know that sinx & cosx both continuous function

⇒p(x) & q(x) is continuous at all real number.

By Algebra of a continuous function

If p(x) & q(x) are continuous for all real numbers.

Then f(x)=p(x)+q(x) is continuous for all real numbers.

∴f(x)=sinx+cosx continuous for all real numbers.

(b) f(x)=sinx−cosx

Let p(x)=sinx & q(x)=cosx

We know that sinx & cosx both continuous function.

⇒p(x) & q(x) is continuous at all real numbers.

By Algebra of continuous function

If p(x) & q(x) are continuous for all real numbers.

Then f(x)=p(x)−q(x) is continuous for all real numbers.

∴f(x)=sinx−cosx is continuous for all real numbers.