# Find the limit question: Kinda confusing.

## Homework Statement

Image here shows the question: ## The Attempt at a Solution

I thought the answer would be limit = infinity

I dont understand how to find the limit to this question.

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jbunniii
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Gold Member

## Homework Statement

Image here shows the question: ## The Attempt at a Solution

I thought the answer would be limit = infinity

I dont understand how to find the limit to this question.
Try simplifying the expression |4 - x| / (x - 4). Consider two cases separately: x < 4 and x > 4.

Thats what I did. I got to x < 4 and x > 4

After that, what do I do?

isnt this undefined?

jbunniii
Homework Helper
Gold Member
Thats what I did. I got to x < 4 and x > 4

After that, what do I do?

What is |4 - x| / (x - 4) when x < 4?

What is |4 - x| / (x - 4) when x > 4?

What is |4 - x| / (x - 4) when x < 4?

What is |4 - x| / (x - 4) when x > 4?
My results were -1

jbunniii
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Gold Member
My results were -1
For both cases? If so, the limit would be -1.

However, you made a mistake in one of the cases.

For both cases? If so, the limit would be -1.

However, you made a mistake in one of the cases.
I did???

jbunniii
Homework Helper
Gold Member
I did???
You did, if you got -1 for both cases.

What does |4 - x| simplify to, if x > 4?
What does |4 - x| simplify to, if x < 4?

What does |4 - x| simplify to, if x > 4?
What does |4 - x| simplify to, if x < 4?

I am sorry, I dont understand :(

I think what is messing me up is the absolute value bars

The absolute value function is defined as:

|a| = -a if a<0
|a| = a if a>=0

This is what you have to work with.

Ahhh...So, then my calc comes out as -1 and 1, therefore it does not equal so its undefined?

jbunniii