Suppose that the temperature at the point (x; y; z) in space is T(x; y; z) =
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Question:
Suppose that the temperature at the point (x; y; z) in space is T(x; y; z) = x2 + y2 + z2. Let a particle follow the right circular helix σ(t) = (cos t; sin t; t) and let T(t) be its temperature at time t.
(a) What is T'(t)?
(b) Find an approximate value for the temperature at t = (π=2) + 0:01.
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