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Lab2C,Ex1,3

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

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Problem1 f @ x _ , y _ , z _ D = 6000 H 1 + H x^2 + y^2 + z^2 L 5 L 6000 1 + 1 5 I x 2 + y 2 + z 2 M u = 8 - 4, - 3, 5 < Sqrt @H - 4 L ^2 + H - 3 L ^2 + 5^2 D : - 2 2 5 , - 3 5 2 , 1 2 > Needs @ "VectorAnalysis`" D SetCoordinates @ Cartesian @ x, y, z DD gradf @ x _ , y _ , z _ D = Grad @ f @ x, y, z DD gradf @ 9, 2, 1 D u gradf @ 9, 2, 1 D .u Cartesian @ x, y, z D : - 2400x I 1 + 1 5 I x 2 + y 2 + z 2 MM 2 , - 2400y I 1 + 1 5 I x 2 + y 2 + z 2 MM 2 , - 2400z I 1 + 1 5 I x 2 + y 2 + z 2 MM 2 > : - 540000 8281 , - 120000 8281 , - 60000 8281 > : - 2 2 5 , - 3 5 2 , 1 2 > 222000 2 8281 Sotheslopein direction H - 4, - 3, 5 L isabout 222000 2 8281 Problem3 v = 8H - 540000 8281 L , H - 120000 8281 L , H - 60000 8281 L< Sqrt @H - 540000 8281 L ^2 + H - 120000 8281 L ^2 + H - 60000 8281 L ^2 D : - 9 86 , - 2 43 , - 1 86 > so:
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