Lab2C,Ex1,3 - Problem 1 f x,y,z 6000 1 u 2 5 1 5 6000 1 x^2...

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Unformatted text preview: Problem 1 f x ,y ,z 6000 1 u 2 5 1 5 6000 1 x^2 y^2 z^2 5 x2 4, 2 , y2 3, 5 z2 Sqrt 1 , 2 2 4 ^2 3 ^2 5^2 3 5 Needs " VectorAnalysis` " SetCoordinates Cartesian x, y, z gradf x , y , z Grad f x, y, z gradf 9, 2, 1 u gradf 9, 2, 1 .u Cartesian x, y, z 2400 x , 1 1 5 2400 y , 1 60 000 , 8281 1 , 1 5 2400 z z2 2 x2 , y2 z2 2 x2 y2 1 1 5 x2 y2 z2 2 540 000 8281 2 5 222 000 8281 2 2 , 5 120 000 8281 3 2 2 222 000 So the slope in direction Problem 3 v Sqrt 9 , 86 9 so : 86 as Du f a when cos Θ , 43 fa 43 2 , 86 cos Θ 4, 3, 5 is about 8281 2 540 000 8281 , 120 000 8281 , 60 000 8281 540 000 8281 ^ 2 120 000 8281 ^ 2 60 000 8281 ^ 2 2 , 86 1 is the largest increase in temperature . 1 0, the change rate of temperature will be zero at that direction. So the from 9 2 , 86 43 , 86 1 the point 9, 2, 1 directions to all plane with a normal vector and pass through point 9, 2, 1 will let the space ship remain the same temperature . ...
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