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Sketch the graph of an example of a function $f$ that satisfies all of the given conditions.$$\lim _{x \rightarrow 2} f(x)=-\infty, \quad \lim _{x \rightarrow \infty} f(x)=\infty, \quad \lim _{x \rightarrow-\infty} f(x)=0$$ $$\lim _{x \rightarrow 0^{+}} f(x)=\infty, \lim _{x \rightarrow 0^{-}} f(x)=-\infty$$

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Calculus 1 / AB

Chapter 1

FUNCTIONS AND LIMITS

Section 6

Limits Involving Infinity

Functions

Limits

Continuous Functions

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how This little sketch here? Eso I want to check a few things. You can see that the limits as X approaches to I limit s approaches to so as exits approaching this is to right. So as you're approaching, uh, to you can see that the function is sliding tourist. Negative infinity. Right? So as you approach to here like that, the function here is sliding tours. Negative infinity, Because this is this is negative. Infinity this negative infinity for the y values. Right? So you're sliding towards negative infinity. So Ah, this one here is sliding towards negative infinity. Well, the learned as X approaches zero from the left. So this is your right. So as you're approaching zero from the ledges is how this is gonna be, right? So as you're approaching zero from the left Musica Pollution zero from values that are lesser then, uh, zero. Right? So as you're approaching zero from the left, where you hit you hit this infinite loop here that is going towards infinity. Can you see that for the y values? So here, this one is also negative. Infinity, right? Because you hit in here, continue to move forward towards you, then you sliding towards here for the white values, right? And then when you're approaching is zero from the right. Right, So the limit as X approaches zero from the right off the function. Welcome. Pollutions air from the right there. You're approaching like that, right? So if you're approaching like that, then you're gonna hit this curve, right? So, hitting that curve, then where are you going? You go into positive infinity. Why? Because, uh this curve here rises, tours positive infinity as you get closer to zero, right? This is getting close. Urges Europe as he gets close. Such as you know, you're getting positive. Infinity, Can you see that? So what is happening here is this one goes to zero, right? Most of infinity goes to positive infamy because as you getting closer to zero like that, this one rises to infinity. Positive infinity, Right? Good. Now what is the limit? As X approaches Negative infinity. Well, this is how you approach negative infinity. You go this way, right? You're going this way forever. So as you're approaching negative infinity, what has happened? We could have a look at a function. What is happening to the function here. The function is approaching, uh, zero. Right functions approaching zero. So I ask you, the function is the current. That's what I'm trying to see. So as you move here towards the left continues to be forever the curve. Here, look. A current fear. It is approaching the X axis here, which is zero. Right. So the function is approaching zero. Yeah, so it is just an example.

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