1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Temperature at (x,y,z)

  1. Jun 29, 2014 #1
    the temperature at a point in space is [tex]T(x,y,z) = x^2+y^2+z^2[/tex]

    and there is a particle traveling along the helix given by

    [tex]\sigma (t) =(cos(t),sin(t),t)[/tex]

    a) find [tex]T'(t)[/tex]

    [tex]T'(t) = \frac{\partial T}{\partial x} \frac{dx}{dt} + \frac{\partial T}{\partial y}\frac{dy}{dt}
    + \frac{\partial T}{\partial z} \frac{dz}{dt}[/tex]

    [tex] = -2cos(t)sin(t) + 2sin(t)cos(t) +2t = 2t [/tex]

    b) find the temperature at time [tex] t = \frac{\pi}{2} + 0.01[/tex]

    [tex] = cos^2 (t) + sin^2 (t) + t^2[/tex]

    evaluated at the given t

    [tex]\approx 3.50 [/tex]

    how does this look?

  2. jcsd
  3. Jun 30, 2014 #2


    User Avatar
    Homework Helper

    The last answer doesn't look right, I mean 1 + t^2, ##\pi^2 \over 4## should be about 2.5, not 3.5.
  4. Jun 30, 2014 #3

    [tex]1+\left( \frac{\pi}{2} + 0.01\right)^2 = 3.49891702681[/tex]
  5. Jun 30, 2014 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    It looks good !
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Temperature at (x,y,z)
  1. F(x, y, z) ? (Replies: 2)

  2. Limit of z = f(x,y) (Replies: 4)