Calculus Volume 1

836

Answer Key

b. Between 600 and 1000 the average decrease in vehicles per hour per lane is −0.0075. Between 1000 and 1500 it is −0.006 per vehicles per hour per lane, and between 1500 and 2100 it is −0.04 vehicles per hour per lane. c.

The graph is nonlinear, with minutes per mile increasing dramatically as vehicles per hour per lane reach 2000. 247 . 1 37 ∫ 0 37 p ( t ) dt = 0.07(37) 3 4 + 2.42(37) 2 3 − 25.63(37) 2 + 521.23 ≈ 2037 249 . Average acceleration is A = 1 5 ∫ 0 5 a ( t ) dt = − 0.7 ⎛ ⎝ 5 2 ⎞ ⎠ 3 + 1.44(5) 2 + 10.44 ≈ 8.2 mph/s

1 | v ( t ) | dt = ⌠ ⌡ 0 t ⎛

⎝ 7 30 t 3 −0.72 t 2 −10.44 t +41.033 ⎞

d ( t ) = ∫

t 4 −0.24 t 3 −5.22 t 3 +41.033 t .

⎠ dt = 7

251 .

Then,

120

0

d (5) ≈81.12 mph ×sec≈119 feet. 253 . 1 40 ∫ 0 40

(−0.068 t +5.14) dt = − 0.068(40)

2 + 5.14 = 3.78m/sec

255 . u = h ( x ) 257 . f ( u ) = ( u +1) 2 u 259 . du =8 xdx ; f ( u ) = 1 8 u 261 . 1 5 ( x +1) 5 + C 263 . − 1 12(3−2 x ) 6 + C 265 . x 2 +1+ C

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