Question

Use the given graph to determine the limit, if it exists

Answer 1

Limit does not exist at x=3.

Explanation:

Using the given graph, we need to check whether the limit exists or not.

From the given graph it is clear that

1. When x approaches to 3 from the left side then function approaches to -1.

2. When x approaches to 3 from the right side then function approaches to -3.

3. When x=3, the value of function is 7.

So, we conclude that

`LHL=\lim\limits_(x\to 3^-)f(x)=-1`

`RHL=\lim\limits_(x\to 3^+)f(x)=-3`

`\lim\limits_(x\to 3)f(x)=7`

Since
`LHL\\eq RHL`, therefore the limit does not exist at x=3.