Find the limit question: Kinda confusing.

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Homework Statement



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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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  • #2
jbunniii
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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 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.
 
  • #3
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Thats what I did. I got to x < 4 and x > 4

After that, what do I do?
 
  • #4
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isnt this undefined?
 
  • #5
jbunniii
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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?
 
  • #6
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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
 
  • #7
jbunniii
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My results were -1

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

However, you made a mistake in one of the cases.
 
  • #8
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For both cases? If so, the limit would be -1.

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

I did???
 
  • #9
jbunniii
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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
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What does |4 - x| simplify to, if x > 4?
What does |4 - x| simplify to, if x < 4?

I am sorry, I dont understand :(
 
  • #11
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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
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Ahhh...So, then my calc comes out as -1 and 1, therefore it does not equal so its undefined?
 
  • #14
jbunniii
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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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