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ww6 - Jignesh Patel due at 11:59pm EDT Assignment 6 MATH262...

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Jignesh Patel Assignment 6 MATH262, Fall 2010 due 10/31/2010 at 11:59pm EDT. . 1. (1 pt) Match the surfaces with the verbal description of the level curves by placing the letter of the verbal description to the left of the number of the surface. 1. z = 2 x + 3 y 2. z = xy 3. z = x 2 + y 2 4. z = ( x 2 + y 2 ) 5. z = 2 x 2 + 3 y 2 6. z = ( 25 - x 2 - y 2 ) 7. z = 1 x - 1 A. a collection of concentric ellipses B. two straight lines and a collection of hyperbolas C. a collection of unequally spaced concentric circles D. a collection of equally spaced parallel lines E. a collection of unequally spaced parallel lines F. a collection of equally spaced concentric circles 2. (1 pt) Find the limit, if it exists, or type N if it does not exist. lim ( x , y ) ( 0 , 0 ) 3 x 2 5 x 2 + 1 y 2 = 3. (1 pt) Find the limit, if it exists, or type N if it does not exist. lim ( x , y ) ( 0 , 0 ) ( x + 23 y ) 2 x 2 + 23 2 y 2 = 4. (1 pt) Find the limit, if it exists, or type N if it does not exist. (Hint: use polar coordinates.) lim ( x , y ) ( 0 , 0 ) 10 x 3 + 3 y 3 x 2 + y 2 = 5. (1 pt) Consider the function defined by F ( x , y ) = xy ( 2 x 2 - 2 y 2 ) x 2 + y 2
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