818
Answer Key
4.53 . 2.93 sec, 64.5 ft Section Exercises 1 . 8 3 . 13 10 5 . 2 3 ft/sec 7 . The distance is decreasing at 390mi/h. 9 . The distance between them shrinks at a rate of 1320
13 ≈ 101.5 mph.
11 . 9
2 ft/sec 13 . It grows at a rate 4 9 ft/sec 15 . The distance is increasing at ⎛
⎝ 135 26 ⎞ ⎠ 26
ft/sec
17 . − 5 6 m/sec 19 . 240 π m 2 /sec 21 . 1 2 π cm 23 . The area is increasing at a rate ⎛ ⎞ ⎠ 8 ft /sec. 25 . The depth of the water decreases at 128 125 π ft/min. 27 . The volume is decreasing at a rate of (25 π ) 16 ft 3 /min. 29 . The water flows out at rate (2 π ) 5 m /min. 31 . 3 2 m/sec 33 . 25 19 π ft/min 35 . 2 45 π ft/min 37 . The angle decreases at 400 1681 rad/sec. 39 . 100 π mi/min 41 . The angle is changing at a rate of 11 25 rad/sec. ⎝ 3 3
43 . The distance is increasing at a rate of 62.50 ft/sec. 45 . The distance is decreasing at a rate of 11.99 ft/sec. 47 . f ′( a ) =0 49 . The linear approximation exact when y = f ( x ) is linear or constant. 51 . L ( x ) = 1 2 − 1 4 ( x −2)
53 . L ( x ) =1 55 . L ( x ) =0 57 . 0.02 59 . 1.9996875 61 . 0.001593
63 . 1; error, ~0.00005 65 . 0.97; error, ~0.0006
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