The temperature T at any point (x, y, z) in space is T = 400xyz2
. Find the
highest temperature on the surface of the unit sphere x
2 + y
2 + z
2 = 1.
10. If u =
x + y
x − y
, v =
x + y
x
, w = x + y + z, determine whether there is a
functional relationship between u, v, w and if so, find it.
11. If u = xey
sin z, v = xey
cos z, w = x
2e
2y
, determine whether there is a
functional relationship between u, v, w and if so, find it.
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