This preview shows page 1. Sign up to view the full content.
Unformatted text preview: d r dt = 2 e 2 t i(sin t ) jt 2 k r (0) =i + j4 k 4. a) Find the domain and range of the function f ( x, y ) = 1 p x 2 + y 29 . 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 + y2 . b) lim ( x,y,z ) (1 ,1 ,1) 2 xy + yz x 2 + z 2 . c) lim ( x,y ) (0 , 0) xyx 2 x 2 + y 2 . 6. Calculate f x , f y and 2 f xy for f ( x, y ) = p x 2 + y 2 . 7. Consider the planes xy + z = 0 and x + yz = 0. Find a parametrization for a line parallel to both planes and one unit distance from each....
View Full
Document
 Fall '06
 PANTANO
 Multivariable Calculus

Click to edit the document details