Unformatted text preview: ) j − t 2 k r (0) = − i + j − 4 k 4. a) (5 points) Find the domain and range of the function f ( x, y ) = 1 p x 2 + y 2 − 9 . b) (5 points) Which of the following properties does the domain satisfy: open, closed, neither open nor closed, bounded, unbounded? c) (5 points) Sketch the level curves f ( x, y ) = 1 4 and f ( x, y ) = 1 √ 7 . 5. Find the limit if it exists: a) (5 points) lim ( x,y ) → (2 , 2) x + y + 4 √ x + y − 2 . b) (5 points) lim ( x,y,z ) → (1 , − 1 , − 1) 2 xy + yz x 2 + z 2 . c) (5 points) lim ( x,y ) → (0 , 0) xy − x 2 x 2 + y 2 . 6. (10 points) Calculate ∂f ∂x , ∂f ∂y and ∂ 2 f ∂x∂y for f ( x, y ) = p x 2 + y 2 . 7. (15 points) Consider the planes x − y + z = 0 and x + y − z = 0. Find a parametrization for a line parallel to both planes and one unit distance from each....
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 Fall '06
 PANTANO
 Math, lim

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