( ) ( ) 46. D = 2sec ⎛ f g x ( ) ( ) (2 ) = = ⎞ 48. D 1 csc csc 1 f g x x x x ⎜ ⎟ 2 2 ⎝ ⎠ ( ) ( ) = ⎛ ⎞ D 2 csc 1 g f x x ( ) ( ) (2sec ) = D 1 g f x x ⎝ ⎠ 2 = sec x 2 segment in two sections, the portion x, across the hall that is 3 feet wide and the y, ( ) ( ) (cot ) portion across that hall that is 4 feet wide. 47. D = −2 = −2 cot f g x x x Then, 49. a. Consider the length of the line θ y = cosθ 3 y x = 3 x cosθ = and 4 θ sin = 4 Thus, = + = + = + 3 4 3secθ 4 cscθ L x y . cosθ θ sin 3 4 b. Let = + . Y1 ( ) ( ) (−2 ) = D cot g f x x cos x _π 25 2 0 0 sin x
46. ( f D g ) ( x ) = 2sec ⎛ 1 x ⎞ 48. ( f D g ) ( x ) = 1 (2 csc x ) = csc x ⎜ 2 ⎟ 2 ⎝ ⎠ ( g D f ) ( x ) = 2 csc ⎛ 1 x ⎞ ( g D f ) ( x ) = 1 (2sec x ) = sec x 2 ⎝ 2 ⎠ 47. ( f D g ) ( x ) = −2 (cot x ) = −2 cot x 49. a. Consider the length of the line segment in two sections, x, the portion across the hall that is 3 feet wide and y, the portion across that hall that is 4 feet wide. Then, cosθ = 3 x x = 3 cosθ and sin θ = 4 y y = 4 θ Thus, L = x + y = 3 + 4 = 3secθ + 4 cscθ . cosθ 3 4 sin θ b. Let Y1 = + . ( g D f ) ( x ) = cot (−2 x ) cos x 25 0 0 sin x _π 2
62514-0132318806_ISM_02-1.docx