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For the function $ A $ whose graph is shown, state the following.

(a) $ \displaystyle \lim_{x\to -3}A(x) $(b) $ \displaystyle \lim_{x\to 2^-}A(x) $(c) $ \displaystyle \lim_{x\to 2^+}A(x) $(d) $ \displaystyle \lim_{x\to -1}A(x) $(e) The equations of the vertical asymptotes

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04:17

Daniel Jaimes

03:30

Gregory Higby

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

J Hardin

July 2, 2021

eh

Campbell University

Oregon State University

University of Nottingham

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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For the function $ A $ who…

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For the function $A$ whose…

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So in this problem we're given this function A has this graph right here and were asked to state the following. So first of all, we're asked to state the limit As X goes to -3 of a f X. And we can see in this graph That -3 over here is actually innocent. Okay. And both the limit As X goes to -3 from the left side of a fx, this goes to infinity and the limit as X goes to minus three from the right side of a of X is also going to infinity. And so therefore the limit his ex goes to money three of a of x is infinity. So the first one is infinity. Now, the next one, the limit as X goes to minus goes to two from the left side they have X. Well, let's look at our graph here for a minute. Here's to and two is also an assam toad here as I go in towards two from the left side, this goes all the way down and keeps continuing on down to minus infinity. Okay, hard to see the limit As X goes to two from the the right hand side of a of X. Well, let's look at our graph again, twos and assam tote and as I come in Towards two from the right hand side, our graph, this asset oats continuing on up towards positive infinity. So this is infinity and then party the limit As X goes to -1 of a of X. Well, let's see As we go to -1 here, Here's -1 right here. And what do we notice this is a vertical asthma tote as well. And whether we come in from The limit as X goes to -1 from the left of a f x is minus infinity, I can draw that better. And that's also the limit As X goes to -1 from the right side of a fx. Because if we look at our graph, both sides Here at -1, go continuing on down to minus infinity. And so the answer for this one is minus infinity. And then part E says equations of the vertical assam. Totes equations of vertical hossam totes. Well, that's everywhere. We have one of those asientos, so that's X equals minus three, X equals minus one, X equals two. Is our three vertical aspect towards that we see occurring here.

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