Is the function defined by f (x) = x 2 – sin x + 5 continuous at x = π?

Question

Philoid · Accepted Answer

It is given that f (x) = x² – sin x + 5

We know that f is defined at x = π

So, at x = π,

f(x) = f(π) = π² -sin π + 5 = π² – 0 + 5 = π² + 5

Now,

Let put x = π + h

If

Thus,

Therefore, the function f is continuous at x = π.

Is the function defined by f (x) = x2 – sin x + 5 continuous at x = π?