Find the limit question: Kinda confusing.

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Homework Help Overview

The discussion revolves around finding the limit of the expression |4 - x| / (x - 4) as x approaches 4. Participants are exploring the implications of the absolute value function in this context.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss simplifying the expression by considering two cases: when x is less than 4 and when x is greater than 4. Questions arise regarding the results of these cases and the behavior of the absolute value function.

Discussion Status

There is an ongoing exploration of the simplification of the absolute value function in different scenarios. Some participants express confusion about the calculations and the implications of the results, while others seek clarification on the definitions involved.

Contextual Notes

Participants note the challenge posed by the absolute value bars and the need to understand the behavior of the function as x approaches the critical point of 4. There is mention of the limits from both sides potentially leading to different values.

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Homework Statement



Image here shows the question:

3538hfq.png


Homework Equations





The Attempt at a Solution



I thought the answer would be limit = infinity

I don't understand how to find the limit to this question.
 
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nukeman said:

Homework Statement



Image here shows the question:

3538hfq.png


Homework Equations





The Attempt at a Solution



I thought the answer would be limit = infinity

I don't 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?
 
nukeman said:
Thats what I did. I got to x < 4 and x > 4

After that, what do I do?

What were your results?

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

What is |4 - x| / (x - 4) when x > 4?
 
jbunniii said:
What were your results?

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

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

My results were -1
 
nukeman said:
My results were -1

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

However, you made a mistake in one of the cases.
 
jbunniii said:
For both cases? If so, the limit would be -1.

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

I did?
 
nukeman said:
I did?

You did, if you got -1 for both cases.

To see what went wrong, please answer these two questions:

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

Your answers shouldn't contain any absolute values.
 
  • #10
What does |4 - x| simplify to, if x > 4?
What does |4 - x| simplify to, if x < 4?

I am sorry, I don't understand :(
 
  • #11
I think what is messing me up is the absolute value bars
 
  • #12
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.
 
  • #13
Ahhh...So, then my calc comes out as -1 and 1, therefore it does not equal so its undefined?
 
  • #14
nukeman said:
Ahhh...So, then my calc comes out as -1 and 1, therefore it does not equal so its undefined?

Correct, the limit from the left doesn't equal the limit from the right, so the overall limit does not exist.
 

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