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

Missouri State University

Campbell University

Baylor University

University of Nottingham

00:56

Felicia S.

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

0:00

00:38

Amy J.

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

alrighty. So we want to find the divergence and the curl of this vector field. So let's just start with the divergence. So that's more or less just this formal dot product where basically, I just add up the partial of each of the component functions of the vector field, taking the corresponding partial derivatives. So this should be the partial with respect to X. So if I call this function p this function que this function are this is p X plus Q Why plus r c. Which is okay, so p, the partial derivative of this with respect to X is going to be too y z. And in the partial derivative of Q, why coordinate function is going to be zero and same for the Z component. If I take the partial with respect Dizzy well, there's no Z, so I get zero. So the divergence is just two y Z And so what's the girl? The curl is going to be? Well, I'm gonna write it. Is this this formal cross product? So we have I j okay. And we have partial partial X partial partial by partial partial Z, and then here I'm gonna put p then Q than our soapy is two x y z que is X squared z and then our is X squared. Y Okay, so what are I dio? I take the partial of this with respect to why? Which is going to be X squared and then minus the partial of this with respect to Z, which is also expert Okay. And then I'll eliminate this and this and I have the partial of this with respect X which is to X y and then the partial. This with respect to Z, which is also to x y, and I notice that I really should have done this minus this. But they're both two x y, which is fine. Two x y minus two x y And then let's see what's the last one? We have partial of this with respect to X, which is to X Z and then minus partial. This with respect to you Why, which is to x Zeke, But notice what happens at any point. X wire and Z, this is just going to be zero. This is just going to be zero, and this is just gonna be zero. So the curl is exactly zero. But what does that tell us? That means that the vector field F is conservative. So in other words, it's path independent. If it represents the force field, it's going to conserve energy. The work done by this force field between two points is going to be independent of which path I choose between those two points. All of that good stuff is going to be true of this factor field, because the curl is zero.

07:28

04:12

10:03

26:52

05:28

06:38

07:48

05:33

28:40

06:44

10:25

08:33

09:29

11:59

07:49

12:44

03:43

04:53