812
Answer Key
289 . −1 291 . 1 2 293 . 1 10 295 . a. v ( t ) = 1
a ( t ) = −2 t ⎛ ⎝ 1+ t 2
⎞ ⎠ 2 c. ( a )0.2, 0.06, 0.03; ( b ) − 0.16, −0.028, −0.0088 d. The hockey puck is
b.
1+ t 2
decelerating/slowing down at 2, 4, and 6 seconds. 297 . −0.0168 radians per foot 299 . a. dθ dx = 10 100+ x 2 − 40 1600+ x 2 b. 18 325
, 9 340 , 42 4745 , 0 c. As a person moves farther away from the screen, the viewing angle is increasing, which implies that as he or she moves farther away, his or her screen vision is widening. d. − 54 12905 , − 3 500 , − 198 29945 , − 9 1360 e. As the person moves beyond 20 feet from the screen, the viewing angle is decreasing. The optimal distance the person should stand for maximizing the viewing angle is 20 feet. 301 . dy dx = −2 x y 303 . dy dx = x 3 y − y 2 x 305 . dy dx = y − y 2 x +4 x +4− x 307 . dy dx = y 2 cos( xy ) 2 y −sin( xy )− xy cos xy
x 2 y − y 3
dy dx = −3
309 .
x 3 +3 xy 2
311 .
y = −1 2
x +2
313 .
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