surface area
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Dr.Peterson
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Please follow our guidelines, by showing what you have been able to do, and asking specific questions about parts you are having trouble with:
What have you been taught about surface areas? Does this look familiar?
https://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx
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What have you been taught about surface areas? Does this look familiar?
https://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx
[MATH]z = f(x, y) = 4 - x - 2y[/MATH]
[MATH]\iint\limits_S dS = \iint\limits_R |\vec{n}| \ dy \ dx = \iint\limits_R |<\frac{-\partial f}{\partial x}, \frac{-\partial f}{\partial y}, 1>| \ dy \ dx = \iint\limits_R |<1, 2, 1>| \ dy \ dx = \iint\limits_R \sqrt{1^2 + 2^2 + 1^2} \ dy \ dx = \sqrt{6} \iint\limits_R \ dy \ dx[/MATH]
I stole this method from someone. Is this correct? What should I do next?
[MATH]\iint\limits_S dS = \iint\limits_R |\vec{n}| \ dy \ dx = \iint\limits_R |<\frac{-\partial f}{\partial x}, \frac{-\partial f}{\partial y}, 1>| \ dy \ dx = \iint\limits_R |<1, 2, 1>| \ dy \ dx = \iint\limits_R \sqrt{1^2 + 2^2 + 1^2} \ dy \ dx = \sqrt{6} \iint\limits_R \ dy \ dx[/MATH]
I stole this method from someone. Is this correct? What should I do next?
Dr.Peterson
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What do you get for the integral? (Do you see that it is just an area in the xy plane?)
The method agrees with that in the link I provided, except that the latter doesn't mention a vector n.
The method agrees with that in the link I provided, except that the latter doesn't mention a vector n.
D
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That's the problem with stealing without understanding!
If you plot these you will find the range and the domain.
It is not totally stealing. I posted a similar problem in another forum, and there was a nice girl who gave me this way of solving. I didn't have the opportunity to reply her back because I think I was banned. We don't want to discuss the real reasons for this unfair ban because you wouldn't either believe me. I can't plot because yeah I don't understand. Can you help me and plot?
Dr.Peterson
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Presumably, before being given problems at this level, you learned, as I suggested, to find the area between two curves. That's all this is:
Find the area of the region bounded by [MATH]y = x^2 [/MATH] and [math]y = 1[/MATH].
Since this is your problem to solve, you need to sharpen those old skills and use them. (Technically, we aren't talking about ranges, but about limits of integration.)
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You get a chance, Mario. Make it a good one. Start acting like a student who is actually working on a specific curriculum. Answer questions. Show YOUR work. Do not say, even one more time, "Can you just show me?" (or anything like that) When you ask questions at this level and can't manage to solve a simple inequality, something is wrong and YOU need to fix it. Where are you coming from? What are you studying? Why are there so many lapses in rudimentary material? Start making sense. This is what is asked of you. Don't wave your victim card. Explain yourself.
You're already failing in this thread:
"What should I do next?"
"I don't understand. Can you tell me what are the ranges of xx and yy?"
"Can you help me and plot?"
Do better.
I hope I'm being sufficiently clear.
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I hate to say this, but all of you are brainwashed by topsquark. When he tells you his opinion about someone, it is not necessary true. He and some of you think that I am running a tutoring business. What the heck is that supposed to mean? First, it makes no sense, and second you don't have one single evidence. Even if that was true, it doesn't matter because you have to treat me as one of your students. The truth is that I am an engineering student who is struggling at mathematics, physics, and related subjects. I am studying Calculus III, but the university forced me to take algebra and some other low level subjects besides it because I failed two times. This is why you see a random level of problems from a simple circle to partial differential equations. I didn't have to tell you all of this. I am telling you now because if I don't you will never stop bothering me. When someone else, not Mario, presents a problem, you all rush to help him/her with a thousand of different ways with full details, even if it was a complicated problem. But when Mario presents a simple problem about the radius of the circle, all of you become detectives. He presented partial differential before. It is weird he is presenting a simple circle now. He must be in exam NOW. No no, he is running a business. No no he is cheating, and many many other of these none making sense stuff you keep telling each other. When you don't want to present a solution for a question I asked, just say it, so I don't waste my time spending my whole day running behind you to get a hint for a simple question. I have a lot of problems to solve, so I spend the whole day reading and studying, and I don't want to waste my time with you anymore. You have all failed to accomplish your jobs properly. This is my last message here and in every other forum. You will never see Mario again.
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Only victim, eh? Too bad. We could have learned some mathematics.
I won't spend much on rebuttal, but I'm the one who came up with the Tutoring Service Theory, first. This eliminates most of your argument.
Also, we have yet to see any legitimate work from you, personally - in the dozens of problems you have posted in various places. The work you have shown is borrowed from someone who is doing the work for you. We have tried and tried to elicit a response from you personally. So far, it hasn't happened. You were given full answers to your first few problems. It was only after your failure to respond in any useful way that your perceived abuse began to surface.
We are volunteers, here. What we provide is a valuable service to those who need a little push in the right direction. When we encounter someone who refuses to participate in an interactive conversation, this is generally seen as an abuse of volunteer services.
I do wish you well. I hope you can find a way to learn the required material in a way that suits your learning style. Simply passing out answers and doing all the actual work so it can be copied isn't really the style that is described in the forum guidelines.
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