Chapter 2, Problem 24RE

To determine

To find: Whether the function is continuous at the indicated point.

Answer to Problem 24RE

The function is continuous at the indicated point $x=d$ .

Explanation of Solution

Given information: The domain of $f$ is set of real number and indicated point is $x=a$ . The graph is given below:

  

Calculation:

From the given graph, it can be seen that $y=f\left(x\right)$ is continuous at $x=d$ because the graph is not broken at this point. Also, the left hand limit and right hand limit is same at $x=d$ .

  $\underset{x\to d^{-}}{\lim }f\left(x\right)=\underset{x\to d^{+}}{\lim }f\left(x\right)$

Since the function is continuous the limit also exists at the point. The function is defined at $x=d$ .

  $\underset{x\to a}{\lim }f\left(x\right)=f\left(d\right)$

Therefore, the function is continuous at the indicated point $x=d$ .