Pre-Calc Homework Solutions 230

Pre-Calc Homework Solutions 230 - 230 Chapter 5 Review dy...

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Unformatted text preview: 230 Chapter 5 Review dy dx d dx 2x 0 33. (a) Note that each interval is 1 day 24 hours Upper estimate: 24(0.020 0.021 0.023 0.025 0.028 0.031 0.035) 4.392 L Lower estimate: 24(0.019 0.020 0.021 0.023 0.025 0.028 0.031) 4.008 L 24 (b) [0.019 2 42. 1 t 2 x 1 dt 0 1 t2 1 1 dt 1 (2x)2 1 2 4x 2 1 x 2 1 x2 1 x2 1 2(0.020) 0.035] 2(0.021) 4.2 L ... ... ... 43. c(x) 2(0.031) 25 2 t dt x 50 50 4t1/2 4 1.11) 0) ... 103.05 ft 87.15 ft c(2500) 2(1.11) 0] 4 4 x x 25 34. (a) Upper estimate: 3(5.30 5.25 5.04 Lower estimate: 3(5.25 5.04 4.71 (b) 3 [5.30 2 20 30 2500 50 30 230 2(5.25) 2(5.04) The total cost for printing 2500 newsletters is $230. 44. av(I) 1 (600 600t) dt 14 0 14 1 [600t 300t 2 4800 14 0 14 95.1 ft 35. One possible answer: The dx is important because it corresponds to the actual physical quantity x in a Riemann sum. Without the x, our integral approximations would be way off. 4 0 4 Rich's average daily inventory is 4800 cases. c(t) av(c) 0.04I(t) 1 14 14 36. 4 f (x) dx 0 f (x) dx 4 0 f (x) dx 4 24 24t 24t) dt 1 24t 14 (24 0 12t 2 14 192 0 (x 4 2) dx 0 x 2 dx 4 0 1 2 x 2 0 2x 4 1 3 x 3 Rich's average daily holding cost is $192. We could also say (0.04)4800 192. x [0 37. Let f (x) max f min f 1 16] sin2 x 64 3 0 16 3 45. 0 (t 3 2t 3) dt 1 4 t 4 1 4 x 4 t2 x2 x 3t 0 3x 2 since max sin2 x 1 since min sin x 1 1 0 1 4 x 4 1 4 x 4 x2 x2 4x 2 3x 3x 12x 4 4 16 0 0 3.09131 2 x4 (max f)(1 0) (min f)(1 1 0) 0 1 sin2 x dx 4 sin x dx 2 1 2 3/2 x 4 3 2 Using a graphing calculator, x or x 1.63052. f (x). f (1) f (1) f (1) f (1) 0 1 0 1 1 4 0 4 0 38. (a) av(y) x dx 0 1 16 4 3 0 4 3 46. (a) True, because g (x) (c) True, because g (1) (b) True, because g is differentiable. 0. 0. 0 and g (1) 0. f (1) 0. (d) False, because g (1) (e) True, because g (1) (f) False, because g (1) (b) av(y) 39. 40. dy dx dy dx d dx 1 a 0 a a 0 x dx 1 2 3/2 ax a 3 a 0 2 3/2 a 3 2 2 cos3 x cos3 (7x 2) x 1 (g) True, because g (x) f (x), and f is an increasing function which includes the point (1, 0). d (7x 2) dx 6 3 x4 14x 2 cos3 (7x 2) 1 47. 0 1 x 4 dx x F(1) 3 F(0) dy 41. dx 6 3 t4 dt 48. y(x) 5 sin t dt t ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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