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Find a formula for a function that has vertical asymptotes $ x = 1 $ and $ x = 3 $ and horizontal asymptote $ y = 1 $.

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Missouri State University

Campbell University

Oregon State University

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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this bomb number fifty eight of this tour Calculus eighth edition section two point six Find a formula for a function that has vertical. Hasn't it's X equals one in X equals three and horizontal as do that. Why equals to one So we can begin first with the vertical aspen, toots. An easy way, Tio No, exactly Where to put a bird qassem toe is to make sure that the denominator equal zero when wherever you want to get rid of glass which had to be here we wanted to be at X equals to one and it x equals three. So you have two terms in the denominator experience one an ex ministry. This guarantees that our function undefined it those families meaning that there's at this continuity. And as long as we don't have anything in the numerator that removes this concentrating, then we can be sure that those vertical isn't it remained with classmates. Horizontal has to do with the limit as expert tunes. Ah infinity! And we want this to be equal two one down. Let's work with what we have right now and the denominator we haven't x squared. Every oil is out. X squared mass for X extreme. And then we're just trying to come up with something. The numerator. It makes us limit goto one. As long as we have a function the same degree that will guarantee that our limit exists and is equal to the coefficient. The ratio that coefficients here. And since then, coefficient of our aunt Denominator of the highest order term is one. We're going to leave this this one and this is this makes our limit. It will be equal to one. If we complete this limited of equal to one, which means our workers, our class will be at one, which means that our numerator should be X squared. And then over on we found a function that has two requested at X equals one X equals three and definitely has a horizontal husband. And why close to one

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