Recent content by YayMathYay

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    Lagrange on an Ellipse to find Max/Min Distance

    Just gave it an attempt, and my maximization problem became:Maximize x^{2} + y^{2} + z^{2} subject to x + y - \sqrt{1 - x^{2}} - \sqrt{1 - y^{2}} = 0 Is this correct? If so, do I need to substitute out z in terms of x and y? Because I have a feeling that would make things very complicated..
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    Lagrange on an Ellipse to find Max/Min Distance

    Ah yes, the thought of it passed my mind, but I didn't think it was viable until you pointed it out - thanks! :) As for the constraints, I know the equations of the cylinder and the plane that create it.. but when I try to put them together (i.e., x^{2} + y^{2} = x + y + z), it doesn't seem...
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    Lagrange on an Ellipse to find Max/Min Distance

    Homework Statement Homework Equations Lagrance Multipliers. The Attempt at a Solution This is a pretty dumb question, and I feel a little embarassed asking but.. I know how to do the Lagrange part (I think). I'm assuming you maximize/minimize the distance, \sqrt{x^{2} +...
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    Surface Integral over a Cone - Stokes?

    Urgh, I just didn't want to type it out because I don't know how to use LaTeX and it looks messy. Integrand: 2(x^2 + y^2) dx dy Changed to polar w/: x = sqrt(3) * cos t y = sqrt(3) * sin t New Integrand: 6r dr dt [r from 0 to sqrt(3), t from 0 to 2pi]
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    Surface Integral over a Cone - Stokes?

    Yes. But if I change to polar, I get 18pi, because of the 2 there.
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    Surface Integral over a Cone - Stokes?

    I did, that and my integrand on the right side came out to be 2(x^2 + y^2). But I don't see how to get to the correct answer from that.
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    Surface Integral over a Cone - Stokes?

    I also am trying this formula: But I'm not getting to 9pi.. I'm not sure what the difference between f(x, y, z) and f(x, y, g(x, y)) is.
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    Surface Integral over a Cone - Stokes?

    Homework Statement Homework Equations I'm guessing Stoke's Theorem? However, I'm not sure how to apply it exactly.. The Attempt at a Solution Looking at Stoke's Theorem, I'm still not sure how to apply it. I'm really just lost as to where to begin; is there even a \grad F to take? I know...
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    Taylor Series about exp(-1/x^2)

    I think I will do that. Thanks a lot for your help!
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    Taylor Series about exp(-1/x^2)

    Well I'm at a loss then, since we aren't given that :T Perhaps just something the professor overlooked, I guess.
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    Taylor Series about exp(-1/x^2)

    Well, here are the previous parts.. My answers were 0, 2x^(-3)exp(-1/x^2), and 0 respectively.. so from that, can I just assume that f(0) = f'(0) = 0?
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    Taylor Series about exp(-1/x^2)

    Homework Statement Homework Equations We just learned basic Taylor Series expansion about C, f(x) = f(C) + f'(C)(x - C) + [f''(C)(x - C)^2]/2 + ...The Attempt at a Solution Well the previous few questions involved finding the limit of the function and the derivative of the function as X...
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    3 Vectors from a Common Point onto a Plane

    3, then. Thanks so much! :)
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    3 Vectors from a Common Point onto a Plane

    Ah, so you would you take dot products of these differences with the given expression and prove that it equals zero?
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    3 Vectors from a Common Point onto a Plane

    I was thinking about this, but wasn't sure how to go about this.. since we're not given information about the plane itself. I guess maybe by using the 3 vectors I can piece out the plane? EDIT: As in, \vec A - \vec B, etc. would be parallel to the plane?
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