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For the function $ f $ whose graph is given, state the following.(a) $ \displaystyle \lim_{x \to \infty} f(x) $(b) $ \displaystyle \lim_{x \to - \infty} f(x) $(c) $ \displaystyle \lim_{x \to 1} f(x) $(d) $ \displaystyle \lim_{x \to 3} f(x) $(e) The equations of the asymptotes

a.$\lim _{x \rightarrow \infty} f(x)=-2$b.$\lim _{x \rightarrow-\infty} f(x)=2$c.$\lim _{x \rightarrow 1} f(x)=\infty$d.$\lim _{x \rightarrow 3} f(x)=-\infty$e.$x=1, x=3, y=-2, y=2$

03:43

Daniel J.

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Oregon State University

Harvey Mudd College

Baylor University

Boston College

Lectures

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03:59

So in this problem were asked a series of limits and they were asked for the equations of the assam totes. Okay, so the first one uh let me change colors here. First one is the limit as X approaches infinity uh F of X, which means going out here to the right. Well, we can see that this graph is Becoming an asset going against ass until they're at -2, isn't it? Okay, Next one says the limit as X approaches minus infinity of our function. And again we can see that as we go out here to minus infinity, this graph is approaching positive to liken assam tote there. Okay, then we're asked a limit as X approaches one graph of X. So when we look at this we need to come in from the left and from the right. And both times they're both going towards what towards basel affinity, aren't they? Okay. And then question D says the limit as X approaches three of f of X. Okay, 1, 2, 3. Here's three right here. So we go down this curve coming in from the left and down this curve coming in from the right. Both times. They're both going towards a negative infinity. Then it says to list all of the assam toads. Yeah. Okay, it's equations of the asientos. So, first of all, since we have all both of our limits left and right, going to infinity one as X approaches one, Then x equals one is a vertical assam toe. Okay, Same thing happens for X equals three, doesn't it? We just go to negative infinity. All right then we also can see we have some horizontal have some toads. Y equals two. Like we showed out here on the left for question Me And why equals -2 for the limit as F of X ghost infinity. Positive affinity for question A And so there's all of our ascent oats

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