Question

1-Find equations of the following. 2(x − 9)2 + (y − 1)2 + (z − 8)2...

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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