I can't find the limit absolute value function.

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Homework Help Overview

The discussion revolves around finding the limit of the absolute value function (|x-2|-2)/x as x approaches 1. Participants express confusion regarding the limit's value and the reasoning behind it, noting that the limit is stated to be -1.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants attempt to evaluate the limit by considering cases where (x-2) is greater than or less than zero, leading to different limit values. Questions arise about the behavior of the function near x=1 and whether it is a straightforward "plug-in" problem.

Discussion Status

The discussion includes various interpretations of the limit and the function's behavior. Some participants provide insights into the function's value for x less than 2, while others question the validity of their approaches. There is an ongoing exploration of how to simplify the function near x=1.

Contextual Notes

Participants are navigating the implications of the absolute value function and its behavior around the point of interest, x=1. There is a noted confusion about the conditions under which different limit values are derived.

Vola
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How find the limit of absolute value function?

Hi everybody,

I can't find the limit of (abs(x-2)-2)/x as x-->1.
I know it's (-1) but I don't see how you get to it.
If I take (x-2)>0 I get L=-3,(x-2)<0 I get L=-1.
However according to the graph two sided limit does exist and it's (-1).

Please help
Thanks
 
Last edited:
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Vola said:
Hi everybody,

I can't find the limit of (abs(x-2)-2)/x as x-->1.
I know it's (-1) but I don't see how you get to it.
If I take (x-2)>0 I get L=-3,(x-2)<0 I get L=-1.
However according to the graph two sided limit does exist and it's (-1).

Please help

What happens when x is near 1?

RGV
 
is it just a "plug-in" problem?

(|1-2|-2)/1 => (|-1|-2)/1 => (1-2)/1 =-1?
 
Last edited:
Vola said:
is it just a "plug-in" problem?

(|1-2|-2)/1 => (|-1|-2)/1 => (1-2)/1 =-1?

What is your answer to the question I asked you?

RGV
 
The value of function is negative(?)
 
Vola said:
The value of function is negative(?)

Let me ask it one last time: if f(x) = (|x-2|-2)/x, what would be the simplified formula for f(x) when x is near 1? Don't guess---calculate!

RGV
 
f(x)=-1
 
Good! For all x less than 2, f(x)= -1 so the limit at any x less than two is -1.

If I take (x-2)>0 I get L=-3,(x-2)<0 I get L=-1.
But you don't "take (x- 2)> 0"! That would be x> 2 and you want the limit at x= 1. You can't "go to 1" if keep x> 2.
 
thank you HallsofIvy and Ray
 

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