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# Find the limit or show that it does not exist.$\displaystyle \lim_{x \to \infty}\frac{3x - 2}{2x + 1}$

## $\frac{3}{2}$

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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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