Pre-Calc Homework Solutions 98

# Pre-Calc Homework Solutions 98 - 98 Section 3.6 1 x cos 2 2...

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Unformatted text preview: 98 Section 3.6 1 x cos 2 2 1 x Since the range of the function f(x) cos is 2 2 dy 1 the largest possible value of is . dx 2 d x sin dx 2 dy dx x d x 2 dx 2 d f(g(x)) dx 53. cos (e) 1 1 , , 2 2 f (g(x))g (x) At x 2, the derivative is f (2)g (2) 1 1 ( 3) 3 f (x) 2 f (x) f (g(2))g (2) 1. 54. dy dx d (sin mx) dx (cos mx) (mx) d dx m cos mx m and passes (f) d dx f(x) 2 d f(x) f (x) dx The desired line has slope y (0) through (0, 0), so its equation is y 55. dy dx x d 2 tan 4 dx x sec 2 2 4 2 m cos 0 mx. At x f (2) 2, the derivative is 1 3 1 6(2 2) 1 12 2 2 sec 2 x d x 4 dx 4 2 f (2) 2 8 . 3d (g) 2 d 1 dx g 2(x) d [g(x)] 2 dx 2(5) ( 4)3 2[g(x)] dx g(x) 2g (x) [g(x)]3 y (1) sec 2 4 ( 2)2 . At x 3, the derivative is 10 64 1 5 . 32 d 2 [ f (x) g 2(x) dx The tangent line has slope 1, 2 tan y x 4 and passes through (x 1) 2, or (h) 1 2g (3) [g(3)]3 d dx (1, 2). Its equation is y 2. f 2(x) 1 2 f (x) f(x) f (x) f 2(x) 2 g 2(x) 2 f 2(x) g 2(x)] The normal line has slope equation is y 1 and passes through (1, 2). Its 2, or y 1 (x 1) x 1 2. g 2(x) [2f(x) d f(x) dx 2g(x) g(x)] d dx Graphical support: g(x)g (x) g 2(x) At x 2, the derivative is g(2)g (2) g 2(2) 10 3 f (2) f (2) [ 4.7, 4.7] by [ 3.1, 3.1] (8) 1 3 (2)( 3) 82 22 f 2(2) 10 3 56. (a) d [2 f (x)] dx 2 f (x) 1 2 3 2 . 3 5 3 17 At x d (b) [ f (x) dx 2, the derivative is 2 f (2) g(x)] f (x) g (x) 68 2 17 57. (a) d [5 f (x) dx g(x)] 5 f (x) g (x) At x g (3) 2 5. 5 f (1) (b) 1, the derivative is g (1) 5 d 1 3 8 3 d dx At x (c) d [ f (x) dx 3, the derivative is f (3) g(x)] f(x)g (x) 1. g(x) f (x) At x 3, the derivative is g(3) f (3) (3)(5) 15 ( 4)(2 ) 8 . d f(x)g 3(x) dx f(x) g 3(x) d dx dx g 3(x) f(x) f (x)[3g 2(x)] g(x) 3 f (x)g 2(x)g (x) At x g 3(x) f (x) g 3(x) f (x) g 3(0) f (0) f(3)g (3) 0, the derivative is 3 f(0)g 2(0)g (0) 1 3 3(1)(1)2 d f(x) (d) dx g(x) g(x) f (x) f(x)g (x) [g(x)]2 (1)3(5) 6. At x 2, the derivative is (2) 1 3 g(2) f (2) f(2)g (2) [g(2)]2 74 3 (8)( 3) (2)2 4 37 . 6 ...
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## This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.

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