Business Calc Homework w answers_Part_57

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Unformatted text preview: 31. [2f (x) 2 x) 1 4 y f (x) dx (1 indefinite integral as 2 C x dx x 2 x2 2 x Ce x f (x)] dx 2 Ce x y y (0) 30. [x 2 32. [g (x) 4] dx x g (x) dx Graphical support: C 4 dx (x 2) 4x 2 Since 2 2) 3x C C C is an arbitrary constant, we may write the indefinite integral as 3x C. [ 5, 5] by [ 5, 20] 28. dy dx dy y1 dy y1 33. We seek the graph of a function whose derivative is (2x 1)(y 1) Graph (b) is increasing on [ (2x 1) dx (2x ln y 1 x2 y 1 Ce x 2 sin x is positive, x and oscillates slightly outside of this interval. This is the 1) dx x , ], where sin x . x correct choice, and this can be verified by graphing C NINT x sin x , x, 0, x . x 34. We seek the graph of a function whose derivative is e x . Since e x 0 for all x, the desired graph is increasing for all x. Thus, the only possibility is graph (d), and we may verify that this is correct by graphing NINT(e x , x, 0, x). 2 2 y Ce x x 1 1 2 1 2 y ( 1) C C 2 y 2e x 35. (iv) The given graph looks like the graph of y 2 x satisfies 1 36. Yes, y Graphical support: 37. (a) dy dx 2 dv [ 3, 3] by [ 10, 40] 29. 2t 1 Since 1 4 x) x C x C. 0 4 C C is an arbitrary constant, we may write the indefinite integral as 6t) dt 3t 2 C Initial condition: v f (x) dx (1 6t (2 2t 4 when t C v f (x) dx 1. x is a solution. dv dt v 2x and y (1) C 3t 2 4 1 1 v (t) dt (b) 0 3t 2 (2t 0 t2 t3 4) dt 1 4t 0 6 0 6 The particle moves 6 m. 0 x 2, which Chapter 6 Review 38. 285 40. Set y1 (2 y)(2x 3) and use IMPEULT with intial values x 3 and y 1 and step size 0.1 for 20 points. x y 3 2.9 x 0.6680 2.8 [ 10, 10] by [ 10, 10] 39. Set y1 y cos x and use EULERT with initial values x 0 and y 0 and step size 0.1 for 20 points. 1 0.2599 2.7 0.2294 y 2.6 0.8011 0 0 2.5 1.4509 0.1 0.1000 2.4 2.1687 0.2 0.2095 2.3 2.9374 0.3 0.3285 2.2 3.7333 0.4 0.4568 2.1 4.5268 0.5 0.5946 2.0 5.2840 0.6 0.7418 1.9 5.9686 0.7 0.8986 1.8 6.5456 0.8 1.0649 1.7 6.9831 0.9 1.2411 1.6 7.2562 1.0 1.4273 1.5 7.3488 1.1 1.6241 1.4 7.2553 1.2 1.8319 1.3 6.9813 1.3 2.0513 1.2 6.5430 1.4 2.2832 1.1 5.9655 1.5 2.5285 1.0 5.2805 1.6 2.7884 1.7 3.0643 1.8 3.3579 1.9 3.6709 2.0 4.0057 x x 41. To estimate y (3), set y1 initial values x 0 and y points. This gives y (3) 1 and step size 0.05 for 60 0.9063. 42. To estimate y (4), set y1 with initial values x x2 2y x 1 and y 60 points. This gives y (4) 43. Set y1 e (x x 0 and y 2y and use IMPEULT with 1 y 2) 1 and use EULERT 1 and step size 0.05 for 4.4974. and use EULERG with initial values 2 and step sizes 0.1 and 0.1. (a) [ 0.2, 4.5] by [ 2.5, 0.5]...
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This document was uploaded on 10/31/2011 for the course MAC 2311 at University of Florida.

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