# Evaluating a limit-removable discontinuity?

• bcjochim07
In summary, the conversation discusses evaluating a limit of a vector valued function where there is a potential removable discontinuity. The individual has graphed the function and noticed the discontinuity, but is unsure how to obtain a limit of 0.5. L'Hopital's rule is suggested as a possible solution.
bcjochim07
evaluating a limit--removable discontinuity?

## Homework Statement

I am evaluating the limit of a vector valued function, and one of the pieces I must evaluate is the limit as t approaches 1 of ln(t)/(t^2 -1). I graphed this function on my calculator, and it seems to me that there is a removable discontinuity. However, the expression cannot be factored so terms will cancel out. If I move the cursor around on my calculator, it also appears that the limit is 0.5, but I'm not sure how to obtain that. It's been awhile since I took Calc. I, so could somebody please help me out? Thanks.

## The Attempt at a Solution

You could use L'hopitals rule.

Oh, of course. Thanks. )

## 1. What is a limit-removable discontinuity?

A limit-removable discontinuity is a type of discontinuity that can be removed by taking the limit of the function at that point. This means that the function approaches a finite value on either side of the discontinuity and can be made continuous by redefining the value of the function at that point.

## 2. How do you evaluate a limit-removable discontinuity?

To evaluate a limit-removable discontinuity, you first need to determine the limit of the function at the point of discontinuity. This can be done by plugging in values that approach the point from both sides. If the limits from both sides are equal, then the function has a removable discontinuity and can be evaluated by redefining the value at that point.

## 3. What is the purpose of evaluating a limit-removable discontinuity?

Evaluating a limit-removable discontinuity allows us to make a function continuous at a specific point. This can be helpful in simplifying the function and making it easier to work with. It also helps us better understand the behavior of the function at that point.

## 4. Can a function have multiple limit-removable discontinuities?

Yes, a function can have multiple limit-removable discontinuities. This means that there are multiple points where the function approaches a finite value on either side and can be made continuous by redefining the value at that point.

## 5. Are all discontinuities removable?

No, not all discontinuities are removable. Only certain types of discontinuities, such as limit-removable discontinuities, can be removed by taking the limit of the function at that point. Other types of discontinuities, such as jump discontinuities or infinite discontinuities, cannot be removed and result in a discontinuous function.

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