1 pt Find the gradient of the function f x , y , z ...

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Tom Pickens Math2400 Assignment Section 14.5 due 02/14/2013 at 03:00am MST 1. (1 pt) Find the gradient of the function f ( x , y , z ) = 5 xe y sin ( 2 z ) . grad f =
2. (1 pt) Find the gradient of the function f ( x , y , z ) = xz 2 , at the point ( 1 , 0 , 1 ) grad f ( 1 , 0 , 1 ) = 3. (1 pt) Find the gradient of the function f ( x , y , z ) =
x 4 ln ( zy ) , at the point ( - 1 , e , 1 ) grad f ( - 1 , e , 1 ) = 4. (1 pt) Find the directional derivative of f ( x , y , z ) = xz + y 3 ,
at ( 3 , 1 , 2 ) in the direction of ~ v = ˜ i + ˜ j + ˜ k . f ~ u =
5. (1 pt) Find the directional derivative of f ( x , y , z ) = zy + x 2 at the point ( 1 , 3 , 2 ) in the direction of a vector making an angle of 3 π / 4 with f ( 1 , 3 , 2 ) . f ~ u =
6. (1 pt) Check that the point ( 1 , 1 , 1 ) lies on the given sur- face. Then, viewing the surface as a level surface for a function f ( x , y , z ) , find a vector normal to the surface and an equation for the tangent plane to the surface at ( 1 , 1 , 1 ) .

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