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Pearce_09
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Hello there, I have a few problems with a recent calculus assignment and i was wondering if someone could give me a hand.
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
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