- SUBJECT INDEX

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z


- A -

absolute error, 339
absolute maxima and minima, 278, 283, 315, 515, 538, 620
acceleration, 4, 323-324
accumulated change, 324, 404

approximating with left rectangles, 326-327, 337, 341
approximating with midpoint rectangles, 339, 348
approximating with right rectangles, 327-330, 337, 341
approximating with Simpson's Rule, 346
approximating with trapezoids, 338-339
difference of, 418, 466
errors in approximations, 339
estimating, 370-372
in sine and cosine models, 545, 551
perpetual, 421, 424-425, 466

accumulation function, 361-362, 370, 387, 404-405

and area, 306, 404
derivative of, 379
for lines, 362-365, 377
formulas, 391-392
graphs, 365-368, 372-373
guidelines for sketching, 370

Admiral Byrd, 568, 574
AIDS, 114, 132, 154, 190, 213-214, 463, 693
algebraic method for slope, 208-209
aligning data, 44, 78
American Humane Association, 63-64
amplitude, 512, 514, 551
angle, 498

cosecant, B2
cosine, 503-504, 551, B1, B9
cotangent, B2
initial side, 503, B6
negative, 503, B7
sine, 503-504, 551, B1, B9
tangent, B1, B9
terminal side, 503, B6
angle measure
convention, 501
conversion, 501
degree, 498, 551
minute, 509
notation, 498, 501
patriotic unit, 509
radian, 499-501, 551
second, 509

annual percentage rate, See APR
annual percentage yield, See APY
Antarctic, 568-569, 574, 581
antiderivative, 379, 404-405, 669-670, 677, 689

Exponential Rule, 384, 386
Constant Multiple Rule, 383, 386
Constant Rule, 382, 386
constant term, 394-395, 404
ex Rule, 384, 386
exception to Simple Power Rule, 384, 386
formulas, 381-383, 386, 397
general, 381-382, 387
notation, 381, 387, 405
of sine and cosine functions, 546, 551
of trigonometric models, 546, 551
Simple Power Rule, 382, 386
Sum Rule, 383, 386

approximating

accumulated change, 324-332
area, 404, 412-414
change, 302-305, 315-316, 673
instantaneous rate of change, 173-174, 179, 199
with derivatives, 183-184, 199, 673

APR, 93, 96-97, 135
APY, 93-94, 96, 135
arc, 508
Arctic Circle, 517-518, 519
area

as probability, 467-468
beneath a curve, 322-324, 351-352
between two curves, 412-414, 466
of circle, 339
of histogram, 465-466
of rectangles, 327, 329, 363
of triangle, 324
of trapezoid, 324, 338

arithmetic progressions, 42
AT&T Submarine Systems, 436
autoscaling, 119
average cost, 5
average of a density function, 473
average rate of change, 144, 148-150, 179, 199, 455, 458, 467
average speed, 322-323
average value

of a cycle, 512, 515, 548-549, 551
of a function, 460, 467
of a quantity, 459, 467, 548
of a sine model, 548, 551
of the rate of change, 456-458, 467

 
axes intercepts, 6, 47

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- B -

baby boomers, 344
best fit, 51-53, 80, 619, 655-658
biological stream, 432-434, 466
blood pressure, 361, 464
body-mass index, 607, 611
break-even point, 4, 6
Brentano-Stevens, 683
bx rule for antiderivatives, 384, 386

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- C -

Campbell Soup Company, 521, 534, 544-545, 552-553
capital value, 437
Carbon 14, 425-426
carrying capacity, 684
Carson River, 340, 353, 396
Catolaccus grandis, 585, 613-614, 643
Chain Rule for derivatives, 249-252, 269, 604-605

Form 1, 250-254
Form 2, 252, 254

change

accumulated, 324, 394
and area, 324, 351-352, 412-414, 466
approximating, 302-305, 315-316, 673
average rate of, 144, 148-150, 179, 199, 455
compensating for, 603-604, 612
constant percentage, 74-76, 96, 680
estimating instantaneous rate of, 173-174, 199
in a function, 304-305
in future value, 431
in present value, 432
instantaneous rate of, 156, 158-160, 170-174, 179, 185, 199, 268
percentage, 74-75, 191, 200
percentage rate of, 192, 200
rate of, 44, 66, 179, 199, 228, 268, 526, 551
results of, 324, 404

Circadian Clock Company, 509
circle

slope, 164
tangent line, 163-165
unit, 502, 506-507, 551

circumference, 499-500
Cobb-Douglas, 603-604, 645, 648, 654
Compaq Computer Corporation, 435
compensating for change, 606, 612
competitive products, 615
complementary products, 615
composition, 34-35, 251-252, 269
compound interest, 7, 22-23, 93-94, 135, 204, 563-564, 591-592, 611
concave down/up, 80, 106, 121, 167
constant

graph, 9
multiplier, 383
percentage change, 74-76, 96, 680

Constant Multiplier Rule for antiderivatives, 383-386
Constant Multiplier Rule for derivatives, 237, 239-240
Constant Multiplier Rule for limits, 423
Constant Rule for antiderivatives, 382-286
Constant Rule for derivatives, 239
Constant Rule for limits, 422
constrained optimization, 619, 645-649, 661
constraint curve, 645-647
consumer price index, 52-53, 87, 130, 216, 248, 313
consumers'

expenditure, 286, 442-443, 467
surplus, 442-443, 450, 467
willingness and ability to spend, 439-441, 467

continuous, 20-25, 65, 282
curve/graph, 21, 65, 155-156, 172, 199, 210, 223

information, 21, 65, 155
model, 21
stream, 427

continuously compounded interest, 94-96, 135, 204, 428, 680-683
contour

curve

formulas, 575-576
sketching, 573-574
slope, 594-595, 604-605, 612

farming, 557
graph, 570-571, 577, 612, 621
temperature, 587
simple closed, 621

cosecant, B2
cosine

function, 502, 504, 527, 691
of an angle, 503-504, 551, B1, B9

cotangent, B2
Cotterill, 582
costs

average, 5
fixed, 4, 5
start-up, 4, 5
total, 4, 5
variable, 4, 5

count data, 331, 356
CPI (consumer price index), 52-53, 87, 130, 216, 248, 313
Creative Technology, 435
Crichton, Michael, 490
critical point, 219, 619-622, 642, 661
cross section, 560, 636-637
cross-sectional function/model, 560-563, 612, 636-637
CSX-Conrail, 436
cubic

function/model, 100, 107-109, 123, 136, 695
derivative, 230, 239

cumulative density function, 478-481, 494
curve

constraint, 645-647, 651
continuous, 21, 65, 155, 172, 199, 210, 223
contour, 557-559, 569, 647
normal, 476
sine, 525
smooth, 155, 171, 210-211, 268

cycle, 497-498, 512, 538
cyclic, 511, 525, 551

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- D -

data, 465

aligning, 44, 78
count, 331, 356
cyclic, 511, 551

discrete, 21, 65, 155
distribution, 465

finding, 69, 319
linear, 43
reporting over time intervals, 147, 331
variability, 465

deceleration, 323-324
decreasing, 9
definite integral, 352, 387, 392, 405, 412

and area, 352-354, 387, 392
and area between two curves, 412-414, 466
as a limiting value of sums, 352, 387, 405, 412
evaluating, 392
interpretation, 353
of a piecewise continuous function, 395-398
sum property, 397
symbol, 352, 387, 405

degree, 498, 551
demand curve, 438, 467
density function

cumulative, 478-481, 494
exponential, 475, 494
normal, 468, 476, 494
output, 470, 494
probability, 468-470, 494
uniform, 471, 478, 487, 494

dependent variable, 17
depreciation, 47, 126
derivative, 179-180, 199, 228, 277, 315, 404

algebraic method, 208-209, 268
approximating with, 183-184, 199

Chain Rule, 249-252, 269
Constant Multiplier Rule, 239-240
Constant Rule, 239

existence of, 210, 223-224
financial market meaning, 190
formulas, 229-234, 239, 269
four-step method, 234
general formula, 234, 269
graph, 218, 277, 279-280, 282-283, 289
sketching, 218-222
interpreting, 181-182
limiting value definition, 234
Linear Function Rule, 239
notation, 268, 301
numerical method, 206-207, 268
of accumulation function, 379
of constant, 228, 239
of cosine function, 531, 551
of cross-sectional model, 588, 605
of cubic function, 230, 239
of exponential function bx, 233, 236, 239
of exponential function ex, 230, 236, 239
of linear function, 227-229, 239
of natural log function, 239
of piecewise function, 210-211
of quadratic function, 229
of sine function, 526-527, 551
of sine model, 528, 551
partial, 589, 591, 605, 612, 642
Product Rule, 259, 269
second, 290-293, 315
second, 531, 541, 595, 689
Simple Power Rule, 231, 239
Sum Rule, 241-242, 269
units, 199, 380-381

determinant, 638
Determinant Test, 638-639, 642
deviation, 51, 656-657
diastolic blood pressure, 361, 464
differences

first, 49, 66, 74, 127
of accumulated changes, 418, 466
percentage, 74, 127
second, 101, 127
third, 107

differential, 680
differential equation, 667-669, 695

general solution, 668, 695
numerical estimate of solution, See Euler's method
particular solution, 669, 695
second order, 689, 695
separable, 679, 695

diminishing returns, 275, 296
directly proportional, 670-671
discount rate, 437
discrete, 20-25
data, 21, 155

graph, 21, 65
information, 21, 65, 155
income stream, 431-432

Disney, Walt, 86
distribution

mean of, 473-474, 494
median of, 473, 487
normal, 468, 476-477, 494
of data, 465
probability, 468, 494
standard deviation of, 473-474, 494

domain, 17
Donner Memorial State Park, 14-15
doubling time, 188, 204

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- E -

e, 94-95
effective rate, 93
Empirical Rule, 486-487
end behavior, 121, 123
equilibrium point, 449, 467
error

absolute, 339
deviation, 51, 656-657
in approximating change, 339
round-off, 54-55
squared, 52

Euler, Leonhard, 673
Euler's method, 667, 673-675, 686-687, 695
event, 467
ex Rule for antiderivatives, 384, 386
ex Rule for derivatives, 230, 236, 239
expected value

of a cycle, 512, 515, 548, 551
of density function, 473
expenditure, 286, 442-443, 467
exponential
decay, 73
density function, 475, 494
function/model, 73, 75-76, 93, 103, 135, 660, 695
growth, 73, 76
growth with constraints, 79

Exponential Rule for antiderivatives, 384, 386
Exponential Rule for limits, 423
extrapolation, 50
extreme point, 276, 280, 283, 315, 619-620, 626, 636, 661

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- F -

Fechner, Gustav, 671, 683
first differences, 49, 66, 74, 127
fixed costs, 4, 5
flow rate of income stream, 427-429, 466
frequency, 512, 514
function, 16, 20, 65

accumulation, 361-362, 370, 387, 404-405, 480, 669
adding, 32
average value of, 460, 467, 548
Cobb-Douglas, 603-604, 645-649, 654-655
combining, 32, 65-66
composition, 34-35, 66, 251-252, 269
continuous, 22, 65, 172
cosine, 502, 504, 527, 531, 551, 691
cross-sectional, 560-567
cubic, 100, 108, 123, 136, 695
cumulative density, 478-481, 494
cyclic, 498-511
demand, 438, 467
exponential, 73, 75-76, 93, 103, 135, 660, 695
increasing, 513, 516
input, 17-19, 56, 65, 505, 507, 558
inside, 35, 66, 252, 269, 604
inverse, 30, 65
linear, 66, 121-123, 136, 660, 695
logistic, 79, 82, 95, 123, 135, 318, 684-685, 695
multivariable, 558
natural logarithm, 237, 239, 384
output, 17-18, 65, 505, 558
outside, 35, 66, 251-252, 269, 604
periodic, 511, 514, 516, 526
piecewise, 37, 66, 123, 171, 199, 210-211
polynomial, 100, 136
probability density, 468-470, 494
product, 258
quadratic, 100, 104, 123, 136, 695
rate of change, 218, 289, 324, 373, 526-527, 531, 669
recovering, 380-381, 405
renewal, 433-434
sine, 502, 504-511, 531, 551, 691, 695
subtracting, 32
supply, 445-448, 467
survival, 433-434
three-dimensional, 560
trigonometric, 497, 502, 504, B1-B2

four-step analytic method, 234
Fundamental Theorem of Calculus, 321, 379, 390, 391, 404, 411, 481
future value, 97, 135

of income stream, 427-428, 466
of biological stream, 434, 466

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- G -

Galileo, 690
Gateway Arch, 469-470
general antiderivative, 381-382, 387
general solution, 668
geometric progression, 42, 72
Girl Scouts, 62
gradians, 499
graph

accumulation, 673
constant, 9
continuous, 21, 65, 155, 172, 199, 210, 223
contour, 557-559, 569
cosine, 527
decreasing, 9, 219
derivative, 218, 277, 279-280, 282-283, 289
discrete, 21, 65
histogram, 465-457, 494
increasing, 9, 219
piecewise, 37, 66, 123, 171-172, 199, 282
rate of change, 218
sine, 505-507, 531
slope, 159, 179, 199, 218, 268, 277, 378-379
smooth, 155, 171, 210-211, 268
steepness of, 47, 49, 160, 220
three-dimensional, 557-560, 569, 612, 638

Gross Domestic Product (GDP), 275, 288, 302
Gross National Product (GNP), 681-683
growth

exponential, 73, 76, 680
exponential with constraints, 79, 82
linear, 42-44
logistic, 79, 82

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- H -

half-life, 73
Halley Bay , 580-581
histogram, 465-467, 494
Hookeís Law, 693-694
horizontal limiting value, 79, 82, 95, 219
Houghton Mifflin Company, 46-47, 178
Hutterite Brethren, 581-582

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- I -

improper integral, 421, 424-425, 466
income stream

continuous, 427, 466
discrete, 431-432, 466
future value, 427-428, 466
present value, 430, 466

increasing, 9, 513, 516
independent variable, 17
index

body mass, 607, 611
consumer price, 52-53, 87, 130, 216, 248, 313
Poynting, 543
Suaerbeck, 544, 552

inflection point, 80, 109, 121, 167, 169, 199, 218, 289, 294-296, 315, 513, 516, 538-541
information

continuous, 21, 65, 155
discrete, 21, 65, 155

initial condition, 669, 673
input, 17-19, 56, 65, 505, 507, 558
interval

input axis

between, 147
from...through, 147
from...to, 147

time, 331

input/output diagram, 17, 33, 66, 291, 505, 558, 563
inside function, 35, 66, 251-252, 269, 604
instantaneous rate of change, 156, 158-160, 179, 268

and time, 185
estimating, 173-174, 199
existence of, 170-173, 210, 223-224

integral

definite, See definite integral
improper, 421, 424-425, 466
symbol, 352, 381, 387, 405

integration, 404-405
Intel, 88
intercept, 6, 47
interest

compound, 7, 22-23, 93-94, 135, 204, 563-564, 591-592, 611
compounded continuously, 94-96, 135, 204, 428, 428, 680-683

International Game Technology, 58
interpolation, 50
inverse function, 30, 65
inversely proportional, 671
irrational number, 95
isobar, 664
isotherm, 587, 664

Return to Top 

- J, K -

Jefferson National Expansion Memorial National Historic Site, 469
jointly proportional, 683
Jurrasic Park, 490
Kelly Services, 147-149, 194

Return to Top

- L -

label, 56
Lagrange, Joseph, 648
Lagrange multiplier, 647-648, 650, 661
interpreting, 650-651, 661
Lake Tahoe, 151-152, 284-285, 298, 345-346, 555-556
land subsidence, 634
LCI International Telecommunications, 194
leading coefficient, 106
least squares method, 53, 655, 657, 661
left rectangles, 326-327, 337, 341
leveling-off value, 79, 82, 219
limit

Constant Multiplier Rule, 423
Constant Rule, 422
definite integral, 412
Exponential Rule, 423
Negative Power Rule, 423
notation, 95, 421
of secant lines, 165-166, 206, 233-234, 268
of areas of midpoint rectangles, 348-352, 404
of sums, 348-352, 404
rules for evaluating, 422-424
Sum Rule, 423
with compound interest, 95, 135
with e, 95
with improper integral, 421, 466
with income streams, 428
with logistic model, 79, 82, 95, 120, 684

line

best-fit, 51-53, 80, 657, 661
secant, 146, 148, 165-166, 199, 206, 208
slope of, 46, 66, 227-229, 234-236
tangent, 158, 163-168, 179, 199, 206-209, 304, 316, 647, 661

Linear Function Rule for derivatives, 239
linear function/model, 44-45, 47, 66, 69, 121-123, 136, 660, 695
local linearity, 169-170
logarithm function, 237, 239, 384
logistic

leveling-off/limiting value, 79, 82, 95, 219, 684
function/model, 79, 82, 95, 123, 135, 318, 684-685, 695
slope graph, 219

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- M -

marginal

analysis, 275, 308, 316
cost, 308, 316, 385
productivity of money, 650, 881
profit, 308, 316
revenue, 308-309, 316

market equilibrium, 449, 467
market price, 441-445, 447, 467
mathematical model, 2, 65
mathematical modeling, 2-3, 8, 65
maximum

absolute, 278, 283, 315, 515, 538, 620
local, See relative
relative, 276, 279, 283, 315, 539, 620-621, 636, 638-639, 661

McDonnell Douglas, 333
mean, 473-474, 494
median, 473, 487
method of least squares, 53, 657, 661
midpoint rectangles, 339, 348
minimum

absolute, 278, 442, 283, 315, 515, 538, 620
local, See relative
relative, 276, 279, 283, 315, 539, 620-621, 636, 638-639, 661, 687

Mississippi River, 635
Missouri River, 635
mixed second partial derivatives, 595, 638-639
model

best-fit, 51-53, 80
choosing, 119-128, 136
continuous, 21
cross-sectional, 560-563, 612, 636-637
cubic, 107-109, 120, 136
elements, 56
exponential, 73, 75-76, 93, 103, 135
exponential, 660
label, 56
linear, 44-45, 47, 66, 69, 121-123, 136
linear, 660
logistic, 684-685
logistic, 79, 82, 95, 123, 135, 318
mathematical, 2, 55
piecewise continuous, 37, 66, 123, 171, 199, 210
polynomial, 100, 136
quadratic, 101-103, 107, 136
reporting, 55
rounding, 55
sine, 511-517, 551, 691-692
use, 76
writing, 56

Mt. Everest, 664
multivariable

constrained optimization, 619, 645-649, 661
function, 558, 612
unconstrained optimization, 619, 636-639, 661

Return to Top

- N -

National Rifle Association, 157, 160
natural log function, 237, 239, 384, 660
Natural Log Rule for derivatives, 239
Negative Power Rule for limits, 423
neurons, 523-524
Newton's Law of Cooling, 689
Newton's Second Law, 693-694
nominal rate, 93, 135
normal density function, 476-477, 494
normal distribution, 468, 476-477, 494
notation

derivative, 179-180, 199
integral, 352, 381, 387, 405

number sequences, 42
numerical method for slope, 206
numerical results

accuracy, 54-55, 57, 66
degree, 498-501
guidelines, 57, 66
irrational, 95
rounding, 54-55, 57, 66

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- O -

October Madness, 151
odometer, 498-500
olestra, 622-625, 636-639, 640
optimal point, See extreme point
optimization

least squares, 655-658, 661
multivariable
constrained, 619, 645-649, 661
unconstrained, 619, 636-639, 655-658, 661
single-variable, 276-278, 280, 315

Ornda Healthcorp, 436
output, 17, 18, 65, 558
outside function, 35, 66, 251-252, 269, 604
overhead, 7

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- P -

parabola, 100-101, 136
partial

derivative, 589, 591, 605, 612, 638
second, 594-596, 638
rate of change, 588-591, 593, 612

particular solution, 669
Passel and Siple, 568-569, 574, 576, 600
patriotic unit (PU), 509
pectin, 585, 610, 644
PepsiCo, 435
peptides, 643-644
percentage

change, 74-75, 191, 200, 680
differences, 101, 127
rate of change, 44, 66, 179, 199, 228, 268

period, 511, 513-514, 516, 551
periodic function, 511, 514, 516, 526
perpetual accumulation, 421, 424-425, 466
piecewise continuous function, 37, 66, 123, 171, 199, 210-211
pigment, 585, 610
plot, See scatter plot
point

break even, 4, 6
critical, 218, 619-622, 642
equilibrium, 449, 467
extreme, 276, 280, 283, 315, 619-620, 626, 636, 661
of diminishing returns, 435, 459, 490
of inflection, 80, 109, 121, 167, 169, 199, 218, 289, 294-296, 315, 513, 516, 538-541
of least rapid change, 289
of most rapid change, 289
of tangency, 158
saddle, 619-622, 624, 661
shutdown, 445

polio, 91
polynomial function/model, 100, 136
Power Rule, See Simple Power Rule
Poynting's index, 543
present value, 97-98, 135

of income stream, 430, 466

principal, 22
probability, 467, 469-470, 494

and proportions, 467
as a percentage, 468
distribution, 465, 470, 494
histogram, 467
interpretation, 467-468, 470
notation, 469

probability density function, 468-470, 494

exponential, 475, 494
mean, 473-474, 494
median, 473, 487
normal, 476-477, 494
output, 469-470, 494
standard deviation, 473, 494
uniform, 471, 494

probability distribution, See probability density function
producers'

surplus, 447-448, 467
total revenue, 447-448, 467
willingness and ability to receive, 447-448, 467

product of functions, 258
Product Rule for derivatives, 259, 269
products

competitive, 615
complementary, 615

profit, 4, 5
proportionality, 670

constant of, 670
direct, 670-671
inverse, 671
joint, 683

progression

arithmetic, 42
geometric, 42, 72

PTA organization, 89, 154, 256
purchasing power of U. S. dollar, 41, 118, 195, 246, 266, 390, 690

Return to Top

- Q -

quadratic

function/model, 101-103, 107, 136, 695
leading coefficient, 106

Return to Top

- R -

Rachofsky, Martin, 509
radian, 499-501, 551
radioisotope, 667
Radon-232, 688
random variable, 467, 494
range, 15
rate

annual percentage, 93
effective, 93
nominal, 93
of change, 44, 66, 179, 199, 228, 268
average, 144, 148-150, 179, 199, 455, 458, 467
average value of, 456-458, 467
estimating, 173-174
formulas, 229-234, 239
graph, 218
instantaneous, 156, 158-160, 170-174, 179, 185, 199, 210, 223-224
partial, 588-591, 593, 612
percentage, 192, 200
trigonometric functions, 526-527, 531, 551

recovered function

input/output diagram, 380-381
units, 380-381

recovering a function, 380-381, 405
relative maximum, 276, 279, 283, 315, 539, 620-621, 636, 638-639, 661
relative minimum, 276, 279, 283, 315, 539, 620-621, 636, 638-639, 661, 687
renewal function, 433-434
Reno Air, 58
Restigouche River, 522, 691-692
results of change, 324, 404
revenue, 4, 5, 258, 286

continuous rate of flow, 360
total, 447-448, 467

revolution, 498-501
right rectangles, 327-330, 337, 341
right triangle, 502, B1, B4
rise, 48
rotation, 501-503
rounding, 54-55, 57, 66
Rowan-Robinson, 692
Rule of 72, 204
run, 47
Russell Corporation, 300-301

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- S -

saddle point, 619-622, 624, 661
Samuelson, Paul, 497
Santa Clara Valley, 634
SAT I: Reasoning Test, 465-469, 473, 486
saturation level, 684
Savannah River, 537, 547
scatter plot, 21, 65, 119-121, 222
Sears, 436
secant

line, 146, 148, 165-166, 199, 206, 208
slope, 146, 148, 199, 233-234
of an angle, B2

second derivative, 290-293, 315, 531, 541, 551, 689

units, 290

second differences, 101, 127
second partial derivative, 594-596, 638
second partials matrix, 595-596, 638-639, 661
separation of variables, 679-680, 695
sextant, 502, B3
shift

horizontal, 513-514, 551
vertical, 512, 514

shutdown point, 445
simple closed contour, 621
Simple Power Rule for antiderivatives, 382, 386
Simple Power Rule for derivatives, 231, 239
Simpsonís Rule, 346
simultaneous equations, 638, 650, 657, 682
sine

function, 502, 504-507, 531, 551, 691, 695
model, 511-517, 551, 691-692
of an angle, 503-504, 551, B1, B9

Siple and Passel, 568-569, 574, 576, 600
slope

algebraic method, 208-209
field, 697-699
formulas, 227-234, 239, 269
graph, 159, 179, 199, 218-223, 268
of contour curve, 594, 604-605, 612, 647, 661
of curve, 158, 164, 179, 199
of graph, 159, 179
of line, 46-48, 66, 227-229, 234-236
of piecewise function, 210-211
of secant line, 146, 148, 199, 233-234
of tangent line, 158, 172, 179, 199, 206-210, 268, 532-533, 604-605, 612, 647, 661
trend, 207-208
undefined, 171-172, 223-224

social gain, 449-450, 467
speed, See velocity
SSE, 75, 657, 661
St. Louis Arch, 469-470
standard deviation, 473-474, 494
start-up costs, 4, 5
stationary point, See critical point
steepness, 47, 49, 160, 220, 592
step size, 673
stream

biological, 432-434, 466
income, 427, 431-432, 466

Suaerbeck index, 544, 552
Sum Rule for antiderivatives, 383, 386
Sum Rule for derivatives, 240-241, 269, 529
Sum Rule for limits, 423
Superbike II, 509
supply curve, 445-448, 467
surplus

consumers', 442-443, 450, 467
producers', 447-448, 467

survival function, 433-434
symmetric difference quotient, 173-174, 179, 526

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- T -

tangent

line, 158, 163-168, 179, 199, 206, 304, 316
algebraic method for slope, 208-209, 268
approximating with, 673
construction, 163-164
horizontal, 315
numerical method for slope, 206-207, 268
on a circle, 163, 165
point, 158
slope as a limiting value, 206, 268
slope, 158-160, 167, 172, 199, 223-224, 236, 268, 532-533, 604-605, 612, 647, 661, 673
to constraint curve, 640-647, 661
vertical, 224, 268
of an angle, B1, B9

Technetium-99, 688
technology, 66
Tenet Healthcare Corporation, 436
third difference, 107
tilt, See slope
topographical map, 569, 664
total cost, 4, 5
total revenue, 447-448
total social gain, 449-450, 467
Toys R Us, 193-194
trapezoid approximation, 338-339
trend, 348-349
trigonometric function, 497, 502, 504, B1-B2
input, 505-507
output, 505-507
trigonometry, 497, 502, 504, 551, B3, B6
turn, 498
turnstile, 498

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- U -

ultraviolet radiation, 514-516, 518-519, 545, 548-549, 600
uniform density function, 471, 478, 487, 494
unit circle, 502, 506-507, 551, B6
units

labeling, 56

Uranium 238, 427

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- V -

variable

controlled, 17
costs, 4
dependent, 17
independent, 17
labeling, 56
observed, 17
random, 467, 494

variable costs, 4, 5
velocity, 322-324, 668
Verhulst, 687, 696
Vertical Line Test, 20, 65
Visa cards, 197

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- W -

Washington Monument, 389
willingness and ability to receive, 447-448, 467
willingness and ability to spend, 441, 467
Winnemucca and Esmeralda silver lodes, 455





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