Chapter 14.3, Problem 32AYU

Is $f$ continuous at 5?

To determine

To find: Whether $f$ is continuous at 5.

Answer to Problem 32AYU

Yes.

Explanation of Solution

Given:

Calculation:

Since $\underset{x\to 5^{-}}{\lim }f\left(x\right)=1$ and $\underset{x\to 5^{+}}{\lim }f\left(x\right)=1$; both the left hand and right hand limits are equal.

Again we see that, $f\left(5\right)=1$.

Since all these three values are equal to 1, therefore $f$ is continuous at 5.