Question

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

Answer 1

Answer:

Limit does not exist at x=3.

Step-by-step 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 $LHL\neq RHL$, therefore the limit does not exist at x=3.