Section14_R - Section 14.R Review exercises 1.A 2.A 3.A 4...

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(3.24/08) Section 14.R Review exercises 1. A What is the value of f ( x, y ) = x 2 e y + 2 cos y at (5 , 0)? 2. A Find g (10 , - 2) for g ( x, y ) = x 2 - 10 y 3 . 3. A Draw the level curves h = c of the linear function h ( x, y ) = y - 2 x for c = 0 , ± 2 , ± 4 , ± 6. 4. A Draw the level curves F = c of the function F ( x, y ) = ( y - 1 2 x 2 ) 3 for c = 0 , ± 1 , ± 8. 5. A Draw the level curve of f ( x, y ) = y cos x through the point (0 , 2). What is value of f on this curve? Find the x - and y -derivatives of the functions in Exercises 6 through 11. 6. A z = x 2 y 3 - 3 x 2 y 7. A z = sin x + cos y 8. A z = x 2 e 3 y 9. A f ( x, y ) = (1 + xy ) 5 10. A g ( x, y ) = x ln y - y ln x 11. A h ( x, y ) = e 2 x +3 y 12. A What are q x (0 , 0) and q y (0 , 0) if q ( x, y ) = radicalbig Q ( x, y ), Q (0 , 0) = 9 , Q x (0 , 0) = 10, and G y (0 , 0) = 5? 13. A What is the t -derivative of H ( t ) = h ( t 2 , t 3 ) at t = 1 if h (1 , 1) = 5 , h x (1 , 1) = 3 and h y (1 , 1) = - 4? 14. A What are (a) F (1 , 2), (b) F u (1 , 2), and (c) F v (1 , 2) if F ( u, v ) = f ( u 2 v 3 , 3 u + 7 v ) and z = f ( x, y ) satisfies f (8 , 17) = 10 , f x (8 , 17) = 5 and f y (8 , 17) = - 1? 15. A What are (a) G (0 , 2), (b) G u (0 , 2), and (c) G v (0 , 2) if G ( u, v ) = g ( v sin u, u sin v ) and z = g ( x, y ) satisfies g (0 , 0) = 4 , g x (0 , 0) = 10 and
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