Find limit of the following function

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Homework Help Overview

The discussion revolves around finding the limit of the function as x approaches 2, specifically lim (x->2) ((|x-3|-1)/(x^2 - 4)). The problem involves understanding the behavior of the function near the point of interest and addressing the absolute value in the numerator.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to factor the denominator and manipulate the numerator to simplify the expression. There is mention of approaching the limit from both sides and the potential for an indeterminate form. Some participants express uncertainty about the use of l'Hospital's rule due to it not being covered in class, while others suggest alternative methods for solving the limit.

Discussion Status

The discussion is active, with participants exploring different methods to approach the limit. Some guidance has been offered regarding the treatment of the absolute value and factoring, but there is no explicit consensus on a single method to solve the problem.

Contextual Notes

Participants note that l'Hospital's rule has not been taught in their class, which influences their approach to finding the limit. There is also a consideration of the behavior of the absolute value function near the point of interest.

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Homework Statement



lim (x->2) ((|x-3|-1)/(x^2 - 4) )

http://www.wolframalpha.com/input/?i=lim+%28x-%3E2%29+%28%28|x-3|-1%29%2F%28x^2+-+4%29+%29
^In case the above equation was unclear

Homework Equations


The Attempt at a Solution


I'm not really sure as to how I'm supposed to approach this problem. I know that I have to factor the denominator and do something to the numerator so that something cancels out. I also tried approaching from both sides, but that didn't do anything at all. Can anybody tell me what to do?
 
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Technically this could be an indeterminate form, which means that you could try using l'hospital's rule to go about finding this limit
 
See, I know that I have to do that. The problem is, our class hasn't been taught that rule yet, so I had the notion that there was another way by which I could find the limit. Of course, I'll probably have to email my professor to see if that's the case. Thanks for the clarification!
 
Ya, this could be solved by a different method, but I personally find l'hospital's rule significantly easier. Hope I was of a little assistance at least
 
Could you perhaps tell me what this different method is?
 
Get rid of the absolute value sign :-)

When x is around 2; x-3 <0 so |x-3|=-(x-3)

Factor the denominator after getting rid the absolute value sign and you will arrive at your answer.
 
Yeah, that totally makes sense. I was about to put the sign for (x-3) as negative, but for some reason I didn't solve it completely, which would've given me my final answer. Thanks a lot! =D
 

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