Answer Key
791
15 . y =− x −2 17 . −49 m/sec (velocity of the ball is 49 m/sec downward) 19 . 5.2 m/sec 21 . −9.8 m/sec 23 . 6 m/sec 25 . Under, 1 unit 2 ; over: 4 unit 2 . The exact area of the two triangles is 1 2
(2)(2) = 2.5 units 2 .
(1)(1)+ 1 2
27 . Under, 0.96 unit 2 ; over, 1.92 unit 2 . The exact area of the semicircle with radius 1 is π (1) 2 2 =
π 2
unit 2 .
29 . Approximately 1.3333333 unit 2 31 . lim x →1
f ( x ) =−2≠ lim x →1 +
f ( x ) =2.
f ( x ) does not exist because lim x →1 −
33 . lim x →0 (1+ x ) 1/ x =2.7183 35 . a. 1.98669331; b. 1.99986667; c. 1.99999867; d. 1.99999999; e. 1.98669331; f. 1.99986667; g. 1.99999867; h. 1.99999999; lim x →0 sin2 x x =2 37 . lim x →0 sin ax x = a 39 . a. −0.80000000; b. −0.98000000; c. −0.99800000; d. −0.99980000; e. −1.2000000; f. −1.0200000; g. −1.0020000; h. −1.0002000; lim x →1 (1−2 x ) =−1 41 . a. −37.931934; b. −3377.9264; c. −333,777.93; d. −33,337,778; e. −29.032258; f. −3289.0365; g. −332,889.04; h. −33,328,889 lim x →0 z −1 z 2 ( z +3) =−∞ 43 . a. 0.13495277; b. 0.12594300; c. 0.12509381; d. 0.12500938; e. 0.11614402; f. 0.12406794; g. 0.12490631; h. 0.12499063; ∴ lim x →2 1− 2 x x 2 −4 =0.1250= 1 8 45 . a. −10.00000; b. −100.00000; c. −1000.0000; d. −10,000.000; Guess: lim α →0 + 1 α cos ⎛ ⎝ π α ⎞ ⎠ =∞, actual: DNE
f ( x ) =+∞
lim x →−2 +
47 . False;
f ( x ) =5.
f ( x ) =2 and lim x →6 +
f ( x ) DNE since lim x →6 −
49 . False; lim x →6
51 . 2 53 . 1 55 . 1 57 . DNE 59 . 0 61 . DNE
63 . 2 65 . 3
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