Unformatted text preview: 4. (a) f x (2 , 1) = 2 , f y (2 , 1) =5 , f (2 , 1) = 1 so z = 1 + 2( x2)5( y1). (b) f (2 . 01 , . 99) ∼ 1 + 2(2 . 012)5( . 991) = 1 . 07. 5. ( a ) Df ( x, y ) = 2 xy 22 xy 2 y 1 3 ( b ) D ( f ◦ g )(3 ,1) = Df (2 , 1) Dg (3 ,1) = 34 2 1 3 ± 12 21 ² = 52 42 75 6. (a) ∇ f (1 , 2 ,1) = (3 ,12 , 12) so D v f (1 , 2 ,1) = (3 ,12 , 12) · (1 / 3 ,2 / 3 , 2 / 3) = 17. (b) 3( x1)12( y2) + 12( z + 1) = 0....
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 Spring '08
 staff
 Algebra, Vectors, Limit, normal vector, different directions.

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