Index 727Darboux sums and integrals, 344-
353
Decimal system, 2, 321-322
Decimals "represent" numbers,
334-339
Decreasing function, 115, 294-313
Dedekind axiom, 313, 344
Dedekind partition, 313
Definite integrals, 252
Del (operator V), 561, 566
Delta (5) is distance, 6
Delta (Ax, Ay, Az, Ow), 116
Demand curves, 333-334
Density 3, 260, 268, 677, 697, 706
Density function, 260
Dependent vectors, 58
Derivative(s), 153
basic formulas for, 154-158, 165,
167
chain rule for, 166
change of order of, 556-559
definition of, 153
directional, 564, 566, 585
of elementary functions, 166
of exponentials, 165, 493
four-step rule for, 154
generalized, 323, 619
of higher order, 170, 179, 304-
313
of hyperbolic functions, 506-
509
integrals of, 333, 659
of integrals, 225, 234-235, 562,
573, 658
intermediate-value property of,
333
of inverse functions, 459-464
of logarithms, 165, 493
notations for, 153, 163-164
partial, 553-586
of powers, 157, 493
as rates, 176-193
as slopes, 168, 285
tables of, 165, 167, end papers
Derivative(s), of trigonometric
functions, 161, 165, 441-443
of vectors, 178
as velocities, 178
Desargues theorem, 110
Determinants, 87-97, 98
Diameter(s), of parabola, 359
of set, 668
Difference (Ax, Ay, Az, Arc). 116
Difference quotients, 153
Differentiable at x [f(x) exists],
153
Differentiable functions, 158, 324-
334
Differential(s), 193-201, 568
Differential equations, 208-210,
445-447, 465, 496-497, 545
partial, 559-560
Differentiation, technique for, 158
Direction angles, 68
Direction cosines, 68
Directional derivative, 564, 566,
5 85
Directrix of conic, 27, 363
Discontinuous derivatives, 350, 561
Discontinuous functions, 145-148,
216, 342
Discriminant of quadratic, 396
Disk, 36, 241
Displacement vector, 178
Distance, 3, 24, 34, 61, 69
from point to line, 28
from point to plane, 80
in polar coordinates, 534
Divergence of vector function, 561
Divergent series, 336, 587, 588,
603-604
Division by zero taboo, 4
Divisors of integers, 120, 605
Dizzy dancer function, 118, 132,
142, 151, 215
Domain and range, 113, 116, 121,
459
Dominated series, 591