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Match the vector fields with the plots labeled I-IV:F(x,y) = ~SelectF(x, y) = <1, sin(y)> Select -F(x, Y) = <x- 2,X + 1> Select-_F(x, y) = <Y, 1/x>...

Question

Match the vector fields with the plots labeled I-IV:F(x,y) = ~SelectF(x, y) = <1, sin(y)> Select -F(x, Y) = <x- 2,X + 1> Select-_F(x, y) = <Y, 1/x> Select

Match the vector fields with the plots labeled I-IV: F(x,y) = ~Select F(x, y) = <1, sin(y)> Select - F(x, Y) = <x- 2,X + 1> Select-_ F(x, y) = <Y, 1/x> Select



Answers

Match the vector fields $ \textbf{F} $ with the plots labeled I - IV. Give reasons for your choices.

$ \textbf{F} (x, y) = \langle y, y + 2 \rangle $

So's off. Next four problems, including this one, is a match in apartment. So you've given a battlefield and the textbook asks you Teo matches the formula is the picture. So you need to have the text book to see the picture. So what you are doing this kind of problem, your first look at the former and see what kind of properties you ah, off the vector field. Or what kind of key feature you can see So usually I will see, given effect or feel Ah, no. The key features I'm looking for are usually like Well, well, this hold this of after field, vanish at a certain direction or at what x and the y Ah. Ah, half ex wife, huh? Vanish and certain cord's name, for example, X coordinate or y coordinate X or why? And also things I'm looking at is the quantity and the direction. Obviously, that's those are or a party even better magnitude. I'm looking as those properties. So from someone we're looking at this one, we will notice that I manage You don't respect her in the vector field will be larger with his father away from zero and will be smaller with this when this points getting close to the origin. In addition, ah, you can see that from four were increasing extra corruption. The the X component of the victor will be larger and it will be the same direction as XX is. And on the white eye, Rocha is also for your father away from the original. Be larger in that direction. Although it will be the other side the road all those of actor will be the opposite side Eruption upsell crossing in access. So given all the things I described, which picture well off it all the properties I say. And if you have the tax for you, see the you see all the four pictures and you will see that only a picture in number four. Well, physic description off all the fish was I mentioned. So this one match with a number four

So for this vector field, we can clear See that when exit? Because why? And f x y we'Ll just be y zero which first of all, we can see that it's a factory on ly ng ex direction, so I should be parallel to x axis. So So you look at the picture also for pictures and you can see that which one? Where you draw the line X equals y direction. You you should see a fact on that direction. All the doctors are parallel to Ahab sexes and the only one that match this description. It's number three. So this retro feel should fit number three and then you can you can verify more detail to see if they really match each other than they should.

For all the four fitting parents, this was probably the hardest one to Ah, look. Although if you use a process of elimination and you did three problems before this way you'LL know that this can't be Machu. It's number two. And that's if there's any other way we can. We can see that this one really match with number two. Ah, you're going to see that close I X plus y is some quality that they ever created and one or no one. An ex. When? When you have X very large, this one is unbounded and you can also see that what access? Very large You'LL see that the vector should be should be almost like a captor off Why direction Oh, are the white component of the vector will be very large where X component responded between one and that one So the key feature the look at this on excess large No, you guys know why Component or the J on this Don't confuse x coordinate and vector component j component which is that, like likes white direction will factor Ah, this large And that c which won that match this Dr Feel or which picture that matches this description. And ah, you can see that the number two should be the only one that match this description. And the other things you can also know Thiss does. Ah, because of these properties. Hi. Component is founded. And by looking at all for picture, you can also see that Number two it's so was the only one that match this description.

We have another set off mansion so that they feel is with the picture of problems. And for each of them, we are asked to match a Grady in off a scaler function, too, to a picture. So the first step is to compute the radiant. Unless we can see this factor field as, uh is X y, which is the same. It's a crowd, innit? That means that a given point will be the Simmons of after connecting origin to that point. And as he goes farther and farther away from the original, the Manitou should get larger and larger. So the only rector that from the picture in the textbook satisfies this requirement is number three.


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