(0 ) − /2) f = 86. ( ) ( 90. D f g (π cos /2) − cos ) = cos ⎛ 1 ⎞ x x (π (0 ) f π /2 − = 0 −1 = − 0 ⎝ 2 ⎠ 2 π / 2 π π /2 The average rate of change is − 2 . π π sin ⎛ 1 ⋅ ⎞ − sin ⎛ 1 ⋅ 0 ⎞ / 2 π /2 − 0 (π (0) sin / 4) − sin 87. = π /2 ⎜ 2 2 ⎟ ⎜ ( ) ( ) (cos ) D = 1 = 1 cos (π g f x x x 2 f 2 ⎟ 2 2 = /2) − π (0 ) f = 2 = 2 ⋅ 2 = 2 π π π /2 2 The average rate of change is 2 . π π ⎛ ⎞ (2 (π (0 ) ⎜ 2 ⋅ ⎟ − cos ⋅ /2) − f = ) 88. 0 π /2 − 0 ⎝ ⎠ π / 2 f (π ) − cos cos ( ) ( ) (cos ) 91. D = −2 = −2 cos f g x x x (0) −1 − = = 1 π /2 π /2 = −2 ⋅ = − 2 4 π π The average rate of change is − 4 . π ( ) ( ) (4 ) ( ) ( ) (sin ) 89. D = sin f g x x D = 4 = 4 sin g f x x x ( ) ( ) (−2 ) D = cos g f x x
86. f (π /2) − f (0 ) = cos (π /2) − cos (0 ) 90. ( f D g ) ( x ) = cos ⎛ 1 x ⎞ π /2 − 0 π / 2 = 0 −1 = − 2 ⎝ 2 ⎠ π /2 π The average rate of change is − 2 . π sin ⎛ 1 ⋅ π ⎞ − sin ⎛ 1 ⋅ 0 ⎞ 87. f (π /2) − f (0 ) π /2 − 0 ⎜ 2 2 ⎟ ⎜ 2 ⎟ = π / 2 sin (π / 4) − sin (0) = π /2 2 ( g D f ) ( x ) = 1 (cos x ) = 1 cos x 2 2 = 2 = 2 ⋅ 2 = 2 π /2 2 π π The average rate of change is 2 . π ⎛ π ⎞ 88. f (π /2) − f (0 ) = π /2 − 0 ⎜ 2 ⋅ ⎟ − cos (2 ⋅ 0 ) ⎝ ⎠ π / 2 cos (π ) − cos (0) = = π /2 = −2 ⋅ 2 = − 4 π π The average rate of change is − 4 . π −1 − 1 π /2 91. ( f D g ) ( x ) = −2 (cos x ) = −2 cos x 89. ( f D g ) ( x ) = sin (4 x ) ( g D f ) ( x ) = 4 (sin x ) = 4 sin x ( g D f ) ( x ) = cos (−2 x )
62514-0132318806_ISM_02-1.docx