temperature at (x,y,z)

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?



thanks!