ðŸ’¬ ðŸ‘‹ Weâ€™re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

No Related Subtopics

Amin G.

April 20, 2021

iPhone

Mahmood K.

July 1, 2021

Piedmont College

University of Michigan - Ann Arbor

Boston College

00:59

Andy S.

If $f(x)=x+\sqrt{2-x}$ and $g(u)=u+\sqrt{2-u},$ is it true that $f=g ?$

0:00

Jsdfio K.

00:38

Amy J.

Felicia S.

Create your own quiz or take a quiz that has been automatically generated based on what you have been learning. Expose yourself to new questions and test your abilities with different levels of difficulty.

Create your own quiz

Okay, so this is going to be the second example out of her continuity, Siri's and says determine whether the function is continuous if it is not state where it is discontinuous on the function that we're dealing with is ffx is equal to X plus two over the quantity X squared minus four. So keep in mind when we're talking about continuity. What that even means is that if we're able to draw a function without picking up our pencil, that constitutes, as continues, continuous by kind of like simple definitions means that you should be able to trace the function without picking up a pencil. So if we have a function where we have a couple of ascent jobs here and here, and so the function looks something like this this and this Well, if I'm trying to retrace it and I go like this, there's no way. As much as I try hard, there's no way for me to get to the next part without jumping to this part right here. And even from here, there is no way for me to get to this part without picking up my pencil. I'm jumping, so that's what it would look like for a function speed. It's continuous, and you don't even have to have an entire asset over. You can have a point, a Centobie as opposed to a vertical ascent top and that still work. But if the one thing to be careful, if it's just because there's an acid trip at all, that doesn't necessarily mean that there would be, uh, it would be discontinuous because if you had a horizontal asking top something like this. But your function was something like this that would be okay, because you could totally draw that without being up your pencil, so that would work. So don't exclude. Kind of like too much, basically. Okay, so then, with the function that we're dealing with, it says Ffx is equal to X plus two over X squared minus four, and we know because we have a rational number type of situation where we have a fraction. We know that the denominator cannot equal zero because if the denominator equals zero that would become undefined. We don't want it to be undefined, so let's think about when that denominator would be equal to zero. Well X squared minus four is equal to zero at which points well, in order to find that we could just factor it because this is just a difference of squares, which we know X squared minus y squared will become factored into X minus y and X plus one. So then, from here I can do X minus two and X plus two because essentially what we're doing is taking the square root of both components, and each one is going to become an X and A y so that at this point I could rewrite this function as expose two divided by X minus two X plus two. So then, from here, you can notice that this exposed to on the top exists on the bottom two we have exposed to on the top and that same factor of exposed to on the bottom, which means that they can technically cancel out. But that still means that there's gonna be a point disk, a newt, a singular point discontinuity at that point. So kind of like one of those as symptoms where it looks like an empty circle, but we also have a vertical ascent. Took X is equal to two because of the fact that if you plug in a two into the equation, the bottom will become zero and we can't have that. But yet it doesn't cancel out with the top. So from there we've established that we have discontinuities at X is equal to two and X is equal to negative two. So the function is not continuous, not continuous, right?

Powers and Polynomial

Rational Numbers

Logarithms

Exponential Functions

Trigonometry

03:10

03:15

13:09

09:37

35:42

12:14

31:42

08:32

03:36

04:20

07:37