1-Find equations of the following.
2(x − 9)2 + (y − 1)2 + (z − 8)2 = 10, (10, 3, 10)
(a) the tangent plane
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2-Suppose that over a certain region of space the electrical potential V is given by the following equation.
V(x, y, z) = 4x2 − 3xy + xyz
(a) Find the rate of change of the potential at P(3, 2, 5) in the direction of the vector v = i + j − k.
(b) In which direction does V change most rapidly at
P?
(c) What is the maximum rate of change at P?
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