**Unformatted text preview: **d r dt = 2 e 2 t i-(sin t ) j-t 2 k r (0) =-i + j-4 k 4. a) Find the domain and range of the function f ( x, y ) = 1 p x 2 + y 2-9 . b) Which of the following properties does the domain satisfy: open, closed, neither open nor closed, bounded, unbounded? Why? c) Sketch the level curves f ( x, y ) = 1 4 and f ( x, y ) = 1 √ 7 . 5. Find the limit if it exists: a) lim ( x,y ) → (2 , 2) x + y 6 =4 x + y + 4 √ x + y-2 . b) lim ( x,y,z ) → (1 ,-1 ,-1) 2 xy + yz x 2 + z 2 . c) lim ( x,y ) → (0 , 0) xy-x 2 x 2 + y 2 . 6. Calculate ∂f ∂x , ∂f ∂y and ∂ 2 f ∂x∂y for f ( x, y ) = p x 2 + y 2 . 7. 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
- Multivariable Calculus, lim, lines L1, x2 + y2