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A bird is ying upward with a leaking bag of seaweed The sack initially weights 10 pounds The bag loses 1/10 pound of liquid per minute, and the bird increases its altitude by 100 feet per minute How much work does the bird perform in the rst six minutes (a) (b) 5660 foot-pounds 5500 foot-pounds

The average value of the function f (x) = sin x x on the interval [0, ] is 3 (a) 4 2 (b) 3 2 (c) 2 4 (d) 4 1 (e) 2 The integral that equals the arc length of the curve y 1 x 4, is

x 3,

The Simpson s Rule approximation to the integral with k = 4 is (a) (b) (c) (d) (e) 0881 0895 083 075 087

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 (a), (a), (e), (d), (c), (a), (a), (c), (b), (d), (d), (a), (b), (d), (e), 2 9 16 23 30 37 44 51 58 65 72 79 86 93 100 (c), (c), (a), (b), (b), (d), (b), (b), (c), (e), (a), (e), (e), (b), (a) 3 10 17 24 31 38 45 52 59 66 73 80 87 94 (b), (d), (c), (c), (e), (e), (c), (a), (e), (a), (e), (e), (c), (a), 4 11 18 25 32 39 46 53 60 67 74 81 88 95 (e), (e), (d), (c), (e), (b), (d), (d), (e), (d), (c), (a), (e), (b), 5 12 19 26 33 40 47 54 61 68 75 82 89 96 (e), (b), (c), (a), (c), (d), (c), (d), (d), (d), (e), (c), (c), (a), 6 13 20 27 34 41 48 55 62 69 76 83 90 97 (d), (c), (e), (d), (c), (e), (d), (a), (a), (e), (b), (e), (b), (d),

7 14 21 28 35 42 49 56 63 70 77 84 91 98

(b), (d), (a), (e), (a), (b), (b), (c), (a), (c), (d), (c), (e), (c),

acceleration as a second derivative, 77 adjacent side of a triangle, 26 angle, sketching, 21 angles in degree measure, 20 in radian measure, 19, 21 antiderivative, concept of, 99 antiderivatives, 94 as organized guessing, 94 arc length, 240 calculation of, 241 area between two curves, 116 calculation of, 103 examples of, 107 function, 110 of a rectangle, 103 positive, 114 signed, 111, 116 area and volume, analysis of with improper integrals, 139 average value comparison with minimum and maximum, 238 of a function, 237 average velocity, 67 bacterial growth, 174 Cartesian coordinates, 5 closed interval, 3 composed functions, 40 composition not commutative, 41 of functions, 40 compositions, recognizing, 41 compound interest, 178

concave down, 81 concave up, 81 cone, surface area of, 246 constant of integration, 100 continuity, 64 measuring expected value, 64 coordinates in one dimension, 3 in two dimensions, 5 cosecant function, 26 Cosine function, 182 cosine function, principal, 182 cosine of an angle, 22 cotangent function, 28 critical point, 87 cubic, 16 cylindrical shells, method of, 229 decreasing function, 81 derivative, 66 application of, 75 as a rate of change, 76 chain rule for, 71 importance of, 66 of a logarithm, 72 of a power, 71 of a trigonometric function, 72 of an exponential, 72 product rule for, 71 quotient rule for, 71 sum rule for, 71 derivatives, rules for calculating, 71 differentiable, 66 differential equation for exponential decay, 174 for exponential growth, 174

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