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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

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03:43

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Missouri State University

Baylor University

Idaho 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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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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