Chapter 2, Problem 17RE

To determine

To find: Whether the limit exist on the basis of the graph.

Answer to Problem 17RE

Yes, the limit $\underset{x\to c^{-}}{\lim }f\left(x\right)$ exists.

Explanation of Solution

Given information: The domain of $f$ is set of real number. The graph is given below:

  

Calculation:

The limit of a function exists at a point, if the function is continuous at that point.

From the given graph, observe the left hand limit of $y=f\left(x\right)$ at $x=c$ . It can be seen that at point $x=c$ the function approaches to a value. So, the left hand limit of the function exists at the point.

Therefore, the limit $\underset{x\to c^{-}}{\lim }f\left(x\right)$ exists.