Question

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

A coordinate graph is shown with a horizontal line crossing the y axis at three that ends at the open point 2, 3, a closed point at 2, 1, and another horizontal line starting at the open point 2, -2.

Answer 1

The limit of the function does not exist.

Explanation:

If
`lim_(x\rightarrow c)f(x)\rightarrow L`, then L is the limit of the function at x=c.

The limit of a function exist if left hand limit at a point is equal to the right hand limit at that point.

`lim_(x\rightarrow c^-)f(x)=lim_(x\rightarrow c^+)f(x)`

From the given graph it is clear that the left hand limit of the function is

`lim_(x\rightarrow 2^-)f(x)=3`

The right hand limit of the function is

`lim_(x\rightarrow 2^+)f(x)=-2`

Since
`lim_(x\rightarrow c^-)f(x)\\eq lim_(x\rightarrow c^+)f(x)`, therefore the limit of the function does not exist.

Answer 2

Lim x→2- f(x) = 3
Lim x→2+ f(x) = -2

Lim x→2- f(x) = 3 is different to -2 = Lim x→2+ f(x), then the limit when x tends to 2 does not exist.

Answer: The limit does not exist.