Pre-Calc Homework Solutions 443

Pre-Calc Homework Solutions 443 - Cumulative Review d 2 (y...

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Unformatted text preview: Cumulative Review d 2 (y dx d (sec x) dx 3 2 3 443 29. 2y) 2y 35. At t dy dx 3 :x 1, y , and 3 2 2yy y y sec x tan x, dy/dt dx/dt 3 3 2 3 2 3 3 2 2 3 3 cos ( /3) 2 sin ( /3) 3 2 . sec x tan x , 2y 2 (2y 2)(sec 3 x (2y sec x tan 2 x) 2y sec x tan x (2y 2)2 2 3 2) (sec x sec x tan 2 x) 2 sec 2 x tan 2 x (2y 2)3 (1 3)( 1) (2)(3) (1 3)2 (a) y y (x 3 1) or 0.866x 3.464 x 2 2 3 5 2 3 30. (1 v)u uv x 0 (1 v)2 dx dt dv dt 1 (b) y y (x 1) or 1.155x 1.443 x 31. (a) v a 3t 2 6t 12t 12 9 36. At t 1)(t 3) t 0; t 5 1 or r dy dx 4 :r 4 sec tan 2. 4 4 i i tan sec 2 4 4 j j 2i 2i j and 2j, so that (b) Solve v t 3. 0 for t: 3(t sec 2 2 (c) Right: v 0 for 0 t 1, 3 left: v 0 for 1 t 3 (d) a v 32. For x dy dx 0 at t 3(2)2 1, y 6(1) 1 1 ,y sin 3 3 6 3 6 2 2, and at that instant 12(2) 9 3 m/sec 1 and 12(1) 2(x 4 1) or y 1) or y cos cos 1 x 2 (a) y (b) y y 1 1 1 2 2(x 1 2 2) or y (x 2) or 0.707x C1, x C2, x C2 1. 2 2x 1 1.414x 1 x x 2x 2(3) 2 2 2x 3 2 (a) y (b) y 33. For x dy dx 1 37. With f (x) 3 f (x) x 2x C1 1 (x 2 3 , choose C1, C2 so that 3 3 3 3 3 3 3 6 and 3 6 1 2 3 6 3 4, x 5, x 3 . 3 . (a) y y 6 3 x 3 6 or 0.407x 0.950 [ 3, 6] by [ 1, 5] x 3 (b) y y 6 6 6 3 3 3 3 38. (a) x x x 3 6 x 2 2y 9 0, 2 0 2 0: 2, 2, 3 or 2.458x 2.050 (b) x (c) x 3 (d) Absolute maximum of 2 at x absolute minimum of 0 at x 1 34. (2x) 4 1 (2yy ) 9 0; y 3 2 9x . 4y 3 2 39. According to the Mean Value Theorem the driver's speed at some time was . 111 1.5 At x (a) y y (b) y 1, y 3 74 mph. , the slope is y 3 2 3 3 2 3 x 2 3 3 2 2 3 (x 3 1) or 0.866x 1) 1.155x 1.443 3.464 2 2 3 (x 5 3 2 or y x ...
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