5

Is $z=-0.2 i$ in the Julia set?...

Question

Is $z=-0.2 i$ in the Julia set?

Is $z=-0.2 i$ in the Julia set?



Answers

$z^{\prime \prime}-x^{2} z=0$

So the question is to find the love that's transform of the Given three linear equations. These are ex dash minus, move I close to zero at X zero Callister zero X dash minus. Their dash equals 20 Liar zero Callister zero X plus y dash minus radicals to three at their net, zero equals two minus two. Now, like this before stick question. This is second question. And this week her the question are taking the love last Transform the first equation we get as and excess minus X zero minus two y s equals 20 s sex as miners to why nets bulls to zero. Now electric me for the question making love last France From off the second equation, we get s excess minus xx zero minus their desk. Bless their dart zero equals zero. Putting the values weaker. Yes, access my nexus. Zehr nous minus two equals zero. No, let this be 50. Question a kindle up. That's transform. On the third question, we get X nous. Unless that's why s minus wired zero minus is earnest equals 23 whipping the values excess plus s by s minus was said as it will suit. Reluctantly, This 60 equation sold Wins 4th 5th 6th equation We get Xs equals two twice off. Three years minus two on as you y ISS It wants to three s miners toe upon missus square and there s stick close to minus two as the square minus three years less still upon as you. Now, by partial fraction, we get X s equals for six upon sq miners for a bonus. You y s bigger. Three upon this minus. Who upon its the square and service. We get minus two upon this less six up bonus square minus food upon as you now take the love last in worse we get Eckstine equals 2 60 minus two days. Where? Why he falls to three minus duty. Desert D equals two minus toe. Bless 60 minus two. Case where this will be the final answer. So thank you.

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Hello and welcome. We're looking at chapter 12 Section six. Problem 52. This is sketching the graph of Z equals X squared plus two y squared more looking at various domains. So for parts A, the domain we're looking at is negative 3 to 3 on the X and y. So, um, one way we could look at this is, uh, kind of Look at each of the faces. If you can kind of think of negative 3 to 3 on the X and Y, it's kind of like the walls of a room on, so try to see what, um, the level curve kind of on each wall of that room s So let's look at it that way. So, uh, if X is negative three and we have Z equals nine plus two y squared. So this is just a problem. Um, and if we look at why from negative three, the smallest, why could be to the biggest? Why? Could be Well, let's just make a little graph here. So we're looking at a graph of essentially, why and Z So why is between three and negative three? So this is like the wall where X equals technically plus or minus tree because it's gonna be the same result s o if why is three and we have 18 plus, uh, 18 or Sorry, 18 plus nine is 27. So it reaches all the way up to 27 up here. If why is, um zero z is nine. So we can Treschow the best we can there, and then it reaches. That's the minimum there. And then, if why is negative three It goes back up to 27. So it looks like this on our front lawn. If we look at X equals, uh, well, actually, we looked at both Are Max and men for X? Why don't we just look at why now? Those walls s o if, why is plus or minus three, we have Z equals. Um, so the X squared plus nine times two is 18 x squared plus 18. So this is be a pariah ball problem with its vertex at 18. Um and so the max and men of X R. Negative three and three. So, uh, this also reaches up to 27. Uh, since those with that since at thes three and negative three volume values the maximum in. That's where are kind of the corners of our room. If you imagine, uh, should equal the same value as we did when we did over here. We have a problem that looks similar. It just doesn't go as low. So we can have the four walls of our room defined here on If we can get an idea of what's going on inside the room, then we're gonna be in good shape. And we do know what's going on inside the room, because as e changes, we have ellipses here, uh, that are just going as e increases the ellipses air gonna increase in size. So I think we have all the pieces we need. Sketch a graph. Good. So maybe before we do this will sketch a sample ellipse. So if we say the equals, um, I know four. Just look at what the ellipses look like. So if z is four, then my ex intercept would have to be to all right, and negative too. And then my why intercepts would have to be rude to So this is an ellipse. If this isn't my ex and this is my why gonna be wider than it is tall with respect to exploit as it's crap. It's B route, too, and negative route to I didn't scale it particularly well, um thinks that that this is our sample. That's well, Okay, so, um, let's just Ah, cap this off. So this is my ex, my y and my Z. So this would be positive. Three back here would be negative. Three, three and negative three. So So when z is zero, we have an ellipse with radius zero. So it's just gonna be a point. You can put that to start. Uh, when, uh let's see, next thing we should look at maybe our our walls, we could put our walls. So, um, when X is positive three or negative three. We have a parabola that goes from call the top here, 27. Um, it's going to go from the lowest point. Uh uh. Yes. Nine. Lowest point of nine up to that 27. So bear with me all the way to zero like this on. Then it's gonna be similar. Just gonna not go as low for when Why is plus or minus treats all kind of connected here. Try toe not go is low, though. And so on the back wall, it's gonna be the same as the front wall here. Lower. Then we could do the same on this side wall. That doesn't actually look so bad, huh? Eso this goes from zero and kind of reaches out to each of these walls. So, um, I'll go to the corners. That's the least likelihood of me ruining a decent pictures before it kind of looks like, uh, a blanket or something. Maybe an umbrella upside down. So this would be our sketch of that graph. Now, um, we're asked to graph the same thing here, um, over different domains. So hopefully you can see the process you'd used to do that. Um, you could also think of it as, like taking, like, moving the wall. So if I If I'm going from negative one toe, one on the X from here, you hear? Let's say and then negative too. Year two, negative three on the why you could kind of redraw your walls, and it's gonna be a similar. Hey, look a little deaf a little differently, so you can think of it that way, and they use the same process. I did bring three D rafting pictures for you to take it. Peek out real quick. So the 1st 1 here is what I just graft. So you can see. Um, this ISS has all the same key features as our draft. We can see it's from negative 3 to 3. Point that out Negative. 3 to 3 on the x and Y, and this goes toe just past 25 goes up to 27. Um, you can see the same key features there. So this is for part A. This is for part B. Part B was from negative one toe, one on the X and from negative, too 23 on the Why. So that's why it looks a little bit uneven on the Y axis here. Doesn't go up this far because we're not going this far over in the wind direction. Um, that's b See here, Ben. See, here is negative too. Two on the X and the same on the why. So it kind of looks pretty similar to a just not as dramatic doesn't go as high on Lee going to 12 here and then d accepting Here's D de iss negative to two on the X and then negative one toe, one on the Why? So that that's what makes this one look a little bit uneven. A cz Well, all right. Um, so we


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