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  • chutieuthichbeer

    June 14th 2011, 12:20 am
  • 5. Given the function F(x,y,z,t)=xcos(t)+ysin(t)+z(t^2+t-2). Find the points, if any,
    on the curve r(t)=<cos(t), sin(t), t> where this function assumes extreme values.




    7. The temperature at a point P(x,y,z) is given by T=200e^(-x^2-3y^2-9z^2), where T is measured in celsius and x, y, z are in meters.

    a) Find the rate of change in the temperature at the point P(2,-1,2) in the direction toward the point Q(3,-3,3)
    b) In what direction does the temperature increase fastest at P?
    c) Find the maximum rate of increase at P.
    d) In what direction(s) does the temperature has no change at P?


    I have to hand it in tomorrow, so please help me out if you know the answers. (show the answers in the details since I was asked to solve it in details)

  • 8hột_zịt_lộn

    June 14th 2011, 1:47 am
  • sau 16 năm rời xa trường lớp , giờ nhìn cái này chóng mặt quá Laugh of loud

    hông giúp được chú tiểu . đi ra , chúc chú tiểu mau mau được khai sáng Giggling

  • mltr

    June 14th 2011, 2:45 pm
  • The temperature at a point P(x,y,z) is given by T=200e^(-x^2-3y^2-9z^2), where T is measured in celsius and x, y, z are in meters.

    a) Find the rate of change in the temperature at the point P(2,-1,2) in the direction toward the point Q(3,-3,3)
    rate of change = (T(Q)-T(P))/distance from P to Q

    b) In what direction does the temperature increase fastest at P?
    Partial derivative dT/dx, dT/dy, dT/dz ... @P

    c) Find the maximum rate of increase at P.
    examine limits at P

    d) In what direction(s) does the temperature has no change at P?
    no change = rate of change = 0


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