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Field F 1 marks) (0,0) to (Shoy: 4 that along 1 vector 1 field 1 conservative conservative. then curI(F)Use this factshow that { Ce...

Question

Field F 1 marks) (0,0) to (Shoy: 4 that along 1 vector 1 field 1 conservative conservative. then curI(F)Use this factshow that { Ce

field F 1 marks) (0,0) to (Shoy: 4 that along 1 vector 1 field 1 conservative conservative. then curI(F) Use this fact show that { Ce



Answers

Show that $\mathbf{F}=\langle 3,1,2\rangle$ is conservative. Then prove more generally that any constant vector field $\mathbf{F}=\langle a, b, c)$ is conservative.

In this problem of victor field we have to verify that director village conservative and we have given the vector field F of X. Y. Is equal to one divided with X. Y. Multiplied with why I minus X. G. Or we can write it as simply they say why do I can begin sell out and this is one day why they with X I -1 divided with YG from here this term is coefficient of Y. Which is called um and this term is confident of gay which is called an now we have to find partial differentiation of em with respect to Y and partial differentiation of and with respect to X. So partial differentiation of em A simply -1 the world with excess square and partial differentiation of one divide with Y with respect to. So here this really would be zero actually because here we have X. S constant. So this is zero. And this is also, do you hear that zito? So we say that partial differentiation of em with respect to Y is equal to partial differentiation of end with respect to X which is equal to zero. So we say they're director field F of X, Y is conservative. So we have the right answer. As conservative

In this problem of vector field we have to verify that the vector Phyllis conservative and we have given that Director field is F F x Y is equal to one divided with x squared. And they said why I minus X. City? So when we compare it, so M is equal to why divided with excess square and n is equal to minus X divided with extra square which is minus one divided with X. Now we have to find the differentiation of partial differentiation of and with respect to Y and partial differentiation of and with respect to X. No when we differentiated so differentiation of Y is simply one. So this is simply one divide with excess square and differentiation of minus one divided with access minus minus plus. So this is one divide with X square plus one divide with excess square. So now we say that partial differentiation of and with respect to Y is equal to partial differentiation of end with respect to X which is equal to one is divided with texas square. So we say that the function or we say that Director Field F is conservative is conservative. So we have the right answer as conservative

Sweetheart the following field. If he's even by one or X squared Plus why squared and so But remind us, why picks? So you want to know before these little field is conservative, so conservative? Um also these up vector field is they're fine under domain. Very sequel to hard to him. My nose 0.0 because he's Victor Field. Some defined. I got X issue on Why you? Because you're dividing by zero. You cannot by zero what is wrong, Joe. Oh, for knowing whether it's conservatively have to complete the girl so itself conservative is the same us asking. Is the girl off people? Zero. So if it is, he called zero. He's conservative. My role. Is that so? So? Well, since we have only two here, the bonds of one I have to this girl will be carry times they take over the function. If one what was Barschel was a room, uh, respect away minus. You're a partial off. Uh, it's too with respect to X so that also he's, uh, mindless. Please minds. So you go ahead on computer or is the parcel with this? But why want so want his miner's wife or square, That's why square. So you do the pushing through. I'm gonna have golden. Why would respect way off minus? Why? With this too? Why this mine is one that is the bottom. Sex is where? Plus why Square Oh, minus minus. Why so Miles? Minus what times? A 1,000,000,000 people this term with respect. Why? Which is true? What? The body. Bye. The bottom. It's good. X squared plus y squared. Oh, that square. So that these would end up being well. This will become a plus. So is he So two. What? It's a word. 60 square minus y square. It's about himself. Why? Square minus XY squared over next square. Plus why, Squirt? Oh, that squid? No, Um, the dolphin to with respect to X, it's gonna be all too. Mmm. Do this, ex. So you have. Yeah. Look, Biggs over excess square most. Why square? So we'll be ready with top. That is one thems X square blows. Why? Squirt minus. Picked up minus six. I'm serious. We start with respect to X, which is two. Thanks. So you have, uh Mmm. That they write it by hand. The bottom of squared that square then, as you can see here various y squared minus two x squared. But he's now minus X So minus like to square sexy square gives you I'm x a squid a little bit. Uh, these he's the same. We start here, as you can see there, they're both equal saying, however, here are these were computing the difference of these two so that for this case, that difference will be people zero because they're equal. So we're people too, minus k zero, um, sort of these cold. This is indeed called zero go sequel to zero. So will these means that ah, if he's conservative because

In digression we are given were they? But if equals one off on access for less vice where x y x way on they do men for this function is given the medical still artists where upon zero common zero Now they have to see if this function is conservative or not. So moving the words the solution going off If we are going to find firstly, Tikolo fifth will be able to use their minus three. Why? Okay, take up girl formula in tow The It is Dicle from line Jodi So that will be Puerto del by the Lex wind by its this were placed by square minus del by Bell. Why, x by access were left by square. Hey, which would be a Puerto? Why, Dell by dialects one upon excess Where plus y squared minus x del by Adele by one upon excess Well, less bias Where? Okay, that is a quest to why? And to Weps upon That's the square place by square with the power no minus X into Huy upon excess Well plus by square who did public you will. Okay, but it's broken. We have here used the reciprocal rule change rule and the general power. Really? So are resolving this. We were object toe wet by minus the wets by upon it's this where Les y square the little square. Okay, that is a close to zero. And the given function at first coins are with him. Thank you.


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