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Find the limit or show that it does not exist.
$ \displaystyle \lim_{x \to \infty}\frac{3x - 2}{2x + 1} $
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02:39
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 6
Limits at Infinity: Horizontal Asymptotes
Limits
Derivatives
Missouri State 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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Find the limit or show tha…
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Evaluate the limit, if it …
All right. We've got this limit problem. Um We want to find this limit or show that it does not exist. A couple different ways of doing this. Some people like to do uh low petals rule because it's fast. Um I don't like that because limits have to exist before derivatives do. Um Some people like to think about and behavior that's not terrible. Um Actually, if X is growing, I just like to stop it from growing because I don't know what big really big over really big is and that's what we have right now. Um So I'm just gonna make it small. I'm going to divide top and bottom by X. So three x divided by X. three. Um And now I have two times one over X. And then two X divided by X. Two. And then I have one times one over X. And then the only theorem I need for ex growing is as X gets big one over X gets small. You agree with that one divided by a really huge Number is always going to be zero. So then I can plug that theorem into these limits. Right? Um limits can add subtract multiply as long as everything exists. So I have three minus two times zero. Because that thing is going to be zero. When X is big divided by two plus zero. So I'm going to get three minus two times zero divided by two plus zero is 3/2. I think that's the cleanest way to think about this
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