Suppose that the temperature at points inside a room is given by a differentiable
Chapter 3, Problem 38(choose chapter or problem)
Suppose that the temperature at points inside a room is given by a differentiable function T (x, y,z). Livinia, the housefly (who is recovering from a head cold), is in the room and desires to warm up as rapidly as possible. (a) Show that Livinias path x(t) must be a flow line of kT , where k is a positive constant. (b) If T (x, y,z) = x 2 2y2 + 3z2 and Livinia is initially at the point (2, 3, 1), describe her path explicitly.
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