Question

Determine if the lim f(x) exists using the graph below, if it does find its value of it does not explain why x—> 1

Answer 1

Given:

The given function f(x) approaches 0.5 when x approaches 1 from the left.

The given function f(x) approaches 1.5 when x approaches 1 from the right.

Required:

We need to find the limit of f(x).

Step-by-step explanation:

There is a jump discontinuity.

The given function f(x) approaches 0.5 when x approaches 1 from the left.

`Left-\text{hand limit =0.5}`

The given function f(x) approaches 1.5 when x approaches 1 from the right.

`Right-\text{hand limit =1.5}`
`\text{We know that }0.5\\e1.5.`

`Left-\text{hand limit }\\e Right-\text{hand limit.}`

The limit does not exist at x =1 in the given graph.

Final answer:

The limit does not exist at x =1 in the given graph because the left hand-limit is not equal to the right-hand limit.