Hello there, I have a few problems with a recent calculus assignment and i was wondering if someone could give me a hand.(adsbygoogle = window.adsbygoogle || []).push({});

1. Suppose that the temperature at the point (x,y,z) in space is T(x,y,z) = x^2 + y^2 + z^2. Let a particle follow the right-circular helix sigma(t) = (cost, sint, t) and let T(t) be its temperature at time t,

a) What is T'(t)

I thought that since T is the temperature at a point, but the particle travles along the helix i could write

T(t) = (costt, sint, t) = (cost)^2 + (sint)^2 + t^t = 1 + t^2

then T'(t) = 2t

does that make sense?

My next problem i am quite stumped on, and even a slight tap in the general right direction would be much appreciated.

2. Let f and g be functions R^3=>R. Suppose f is differentiable and

(Gradient)f = (partial f wrt x, partial f wrt y, partial f wrt z) = g(x,y,z)(x,y,z)

Show that f is constant on any sphere radius r centered at the origin defined by x^2 + y^2 + z^2 = r^2.

Thanks alot

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# Homework Help: Calculus questions

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