# Find limit of the following function

• Zipzap
In summary, the problem is to find the limit of (|x-3|-1)/(x^2 - 4) as x approaches 2. There are multiple approaches to solving this problem, including using L'Hopital's rule and manipulating the absolute value sign. Ultimately, the solution involves factoring the denominator and taking into account the negative sign for (x-3) when x is close to 2.
Zipzap

## 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

## 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?

Technically this could be an indeterminate form, which means that you could try using L'Hopitals 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'Hopitals 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

## 1. What is the concept of finding the limit of a function?

The limit of a function is the value that a function approaches as the input (x-value) approaches a certain value. It does not necessarily mean the actual value of the function at that point.

## 2. How do I find the limit of a function algebraically?

To find the limit of a function algebraically, you can use various techniques such as factoring, simplifying, or using algebraic manipulation rules. It is important to also check for any potential restrictions or discontinuities in the function.

## 3. Can I find the limit of a function graphically?

Yes, you can find the limit of a function graphically by examining the behavior of the function as the input approaches the desired value. If the function has a removable discontinuity, the limit can be found by evaluating the y-value at that point.

## 4. Is there a difference between a one-sided limit and a two-sided limit?

Yes, a one-sided limit only considers the behavior of the function as the input approaches the desired value from one direction (either from the left or right). A two-sided limit, on the other hand, considers the behavior of the function as the input approaches from both the left and right sides.

## 5. Are there any special cases when finding the limit of a function?

Yes, there are a few special cases to consider when finding the limit of a function. These include limits at infinity, limits of rational functions with horizontal asymptotes, and limits of trigonometric functions. It is important to understand these special cases and how to handle them when finding the limit of a function.

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