Pre-Calc Homework Solutions 124

Pre-Calc Homework Solutions 124 - 124 Chapter 3 Review d...

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Unformatted text preview: 124 Chapter 3 Review d f(1 dx 64. continued iv. If f (x) f (x) f (x) 3 4/3 x 4 (d) 4, then f (x) x 1/3 5 tan x) f (1 5 tan x)( 5 sec 2 x) and At x f (1 1. (e) 0, the derivative is 5 tan 0)( 5 sec 2 0) f (1)( 5) 1 ( 5) 5 1 2/3 x , which contradicts the given equation 3 x 1/3. Answer is D: i and iii only could be true. Note, however that i and iii could not simultaneously be true. 65. (a) d f(x) dx 2 cos x (2 cos x)( f (x)) ( f (x))( sin x) (2 cos x)2 3f (0) 32 2 . 3 At x (2 0, the derivative is cos 0)(f (0)) (f(0))( sin 0) (2 cos 0)2 (f) [ 1, 5] by [ 10, 80] d [10 sin dx (b) t interval [0, 0.5] [0.5, 1] [1, 1.5] [1.5, 2] [2, 2.5] [2.5, 3] [3, 3.5] [3.5, 4] (c) avg. vel. 38 0.5 58 1 70 1.5 74 2 70 2.5 58 3 38 3.5 10 4 10 0 38 0.5 58 1 70 1.5 74 2 70 2.5 58 3 38 3.5 x 2 f (x)] 2 x 10 sin (2f(x)f (x)) 2 x 20 f(x)f (x) sin 5 2 10f 2(x) cos x f (x) cos 2 2 x 2 2 56 40 24 At x 1, the derivative is 2 20 f(1) f (1) sin 20( 3) 12. 1 (1) 5 5 f 2(1) cos 5 ( 3)2(0) 2 8 8 24 40 56 (b) 67. (a) d [3f (x) dx g(x)] 3f (x) g (x) At x 3f ( 1) 1, the derivative is g ( 1) 3(2) 1 5. d 2 [f (x)g 3(x)] dx [ 1, 5] by [ 80, 80] f 2(x) 3g 2(x)g (x) g 3(x) 2f(x)f (x) f (x)g 2(x)[3f(x)g (x) 2g(x)f (x)] At x 0, the derivative is f(0)g 2(0)[3f(0)g (0) 2g(0)f (0)] ( 1)( 3)2[3( 1)(4) 2( 3)( 2)] 9[ 12 12] 0. (c) d g(f(x)) dx (d) Average velocity is a good approximation to velocity. 66. (a) d [ dx g (f(x))f (x) x f (x)] x f (x) 2 1 x f(x) At x 1, the derivative is g (0)f ( 1) (4)(2) 8. At x 1, the derivative is 1 2 1 1 2 f(x) 2 g (f( 1))f ( 1) 1 5 f (x) 2 f (x) f (0) f (0) f ( x) 1 5 1 f (1) d dx f (1) 1 1 ( 3) 2 13 . 10 (d) d f(g(x)) dx f (g(x))g (x) At x (b) f(x) f (x) 1, the derivative is f ( 1)g ( 1) (2)(1) 2. f (g( 1))g ( 1) 2 2 9 1 . 3 At x d f( dx 0, the derivative is d dx (e) d f (x) dx g(x) 2 (g(x) 2)f (x) f(x) g (x) (g(x) 2)2 ( 3 2)( 2) ( 1)(4) ( 3 2)2 (c) x) f ( x) x At x (g(0) 1 . 10 0, the derivative is 2)f (0) f(0)g (0) (g(0) 2)2 At x 2 x f ( 1) f (1) 1, the derivative is 2 2 1 2 6. ...
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