The temperature T at (x,y,z) in the 3D space is given by T(x,y,z) = ln(1+x2y2+z2). a)...

The temperature T at (x,y,z) in the 3D space is given by T(x,y,z) = ln(1+x²y²+z²).

a) Find rate of change of T at the point P(1,-1,-1) in the direction of Q(2,0,0)?

b) In which direction from P(1,-1,-1) does the temperature T increase most rapidly?

c) What is the maximum rate of change of T at P(1,-1,-1)?

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Expert Solution

Colby Messinger answered 1 hour ago

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