810
Answer Key
197 . (2
n +1) π
n is an integer
4 , where
⎛ ⎝ π
⎞ ⎠ ,
⎛ ⎝ 3 π
⎞ ⎠
199 .
4 , 1
4 , −1
201 . a =0, b =3 203 . y ′ =5cos( x ), increasing on ⎛
⎞ ⎠ ,
⎛ ⎝ 3 π
⎞ ⎠ , and
⎛ ⎝ 7 π
⎞ ⎠
⎝ 0, π 2
5 π 2
2 ,
2 , 12
209 . 3sin x 211 . 5cos x 213 . 720 x 7 −5tan( x )sec 3 ( x )−tan 3 ( x )sec( x ) 215 . 18 u 2 ·7=18(7 x −4) 2 ·7 217 . −sin u · −1 8 =−sin ⎛ ⎝ − x 8 ⎞ ⎠ · −1 8 219 . 8 x −24 2 4 u +3 = 4 x −12 4 x 2 −24 x +3 221 . a. u =3 x 2 +1; b. 18 x ⎛ ⎝ 3 x 2 +1 ⎞ ⎠ 2
223 . a. f ( u ) = u 7 , u = x ⎞ ⎠ 225 . a. f ( u ) =csc u , u = πx +1; b. − π csc( πx +1) ·cot( πx +1) 227 . a. f ( u ) =−6 u −3 , u = sin x , b. 18sin −4 x ·cos x 229 . 4 (5−2 x ) 3 231 . 6 ⎛ ⎝ 2 x 3 − x 2 +6 x +1 7 + 7 x ; b. 7 ⎛ ⎝ x 7 + 7 x ⎞ ⎠ 6 · ⎛ ⎝ 1 7 − 7 x 2 ⎞ ⎠ 2 ⎛
⎝ 3 x 2 − x +3 ⎞ ⎠ ⎝ sec 2 x +cos x ⎞ ⎠
233 . −3(tan x +sin x ) −4 · ⎛
235 . −7cos(cos7 x ) · sin7 x 237 . −12cot 2 (4 x +1) ·csc 2 (4 x +1) 239 . 10 3 4 241 . y = −1 2 x 243 . x = ± 6 245 . 10
247 . − 1 8 249 . −4 251 . −12 253 . a. − 200 343 m/s, b.
600 2401 m/s
2 , c. The train is slowing down since velocity and acceleration have opposite signs.
⎛ ⎝ 0.0003 x 2 −0.04 x +3 ⎞
dC dt =100·
255 . a. C ′( x ) =0.0003 x 2 −0.04 x +3 b.
⎠ c. Approximately $90,300 per week
πr 2 ( t +1) 3
b. The volume is decreasing at a rate of − π 36 ft
dS dt = − 8
3 /min.
257 . a.
259 . ~2.3 ft/hr 261 . a.
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