Advanced Engineering Mathematics
Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 9.4, Problem 13E
To determine

To calculate: the first partial derivatives of the given function z=x2xy2+4y5 .

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In Problems 11–20, for the given functions f and g. find: (a) (f° g)(4) (b) (g•f)(2) (c) (fof)(1) (d) (g ° g)(0) \ 11. f(x) = 2x; g(x) = 3x² + 1 12. f(x) = 3x + 2; g(x) = 2x² – 1 1 13. f(x) = 4x² – 3; g(x) = 3 14. f(x) = 2x²; g(x) = 1 – 3x² 15. f(x) = Vx; 8(x) = 2x 16. f(x) = Vx + 1; g(x) = 3x %3D 1. 17. f(x) = |x|; g(x) = 18. f(x) = |x – 2|: g(x) x² + 2 2 x + 1 x² + 1 19. f(x) = 3 8(x) = Vĩ 20. f(x) = x³/2; g(x) = X + 1'
In Problems 2–4, for the given functions fand g find: (a) (f° g) (2) (b) (g • f)(-2) (c) (fo f) (4) (d) (g ° 8) (-1) 2. f(x) = 3x – 5; g(x) = 1 – 2r 3. f(x) = Vx + 2: g(x) = 2x² + 1 4. f(x) = e"; g(x) = 3x – 2
In Problems 39–46, show that (f ° g) (x) = (g° f) (x) = x. %3D 39. f(x) = 2x; g(x) = 40. f(x) = 4x; g(x) = i* 41. f(x) = x; g(x) %3! %3D 43. f(x) = 2x – 6; 8(x) = ; (x + 6) 46. fl+) = s(*) = 42. f(x) = x + 5; g(x) = x - 5 44. f(x) = 4 – 3x; g(x) = (4 - x) %3D 45. f(x) = ax + b; g(x) = - (x - b) a + 0 %3D a
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