INDEX 0 445
Cubic functions:
as contours (level curves), 41.34
graphs of, 5.10, 5.19, 41.34
Curl, 45.28 to 45.31, 45.33, 45.34,
45.36 to 45.38
Curvature (K), 34.94 to 34.101,
34.103,35.108,35.109,45.21
to 45.23
Curves (see Graphs)
Curvilinear motion, 34.43 to
34.108
Cusps in graphs, 15.44
Cycloids:
acceleration vector for, 34.86
arch of, 34.39
curvature (K) of, 34.101
equations of, 34.20
Cylinders:
equations of, 41.26, 41.27, 41.68,
41.83,41.93,41.95,41.97
graphs of, 41.1,41.2
inscribed in cones, 16.43
surface area of, 16.22, 42.89
volume of, 14.2, 14.48, 16.7,
16.8, 16.16, 16.18, 16.43,
43.67, 44.70
Cylindrical coordinates, 41.67 to
41.85
Decay (see Exponential growth
and decay)
Decreasing functions, 11.19 to
11.26
Decreasing infinite sequences,
36.58, 36.61 to 36.63
Definite integrals:
approximating sums for, 20.1,
20.2, 20.5
convergence of, 32.1 to 32.10,
32.23 to 32.27, 32.29, 32.31,
32.41 to 32.44, 32.48, 32.53,
32.54
derivatives of, 20.42 to 20.47,
20.51, 20.73, 20.74, 20.87
exponential functions, 24.45 to
24.49, 24.55, 24.76, 24.92,
24.93,32.6,32.7,32.12to
32.14, 32.17 to 32.22, 32.38,
32.39, 32.58
inverse trigonometric functions,
27.61 to 27.64, 27.81,27.82,
32.54
Laplace transforms, 32.57 to
32.60
natural logarithms, 23.10 to
23.22, 23.53, 23.68, 23.69,
23.79, 23.80, 28.25 to 28.31,
32.4, 32.5, 32.8, 32.10,
32.15,32.16,32.36,32.37,
32.50
Definite integrals (Cont.):
powers or roots, 20.9, 20.12 to
20.14, 20.16 to 20.19, 20.23,
20.25 to 20.32, 20.35 to
20.38, 20.40, 20.57, 20.64,
20.71,20.72, 20.75 to 20.78,
20.91,20.92,23.61, 23.62
trigonometric functions, 20.10,
20.11,20.15, 20.20 to 20.22,
20.24, 20.39, 20.49, 20.60,
20.62, 20.63, 20.79 to 20.84,
28.32 to 28.34, 28.53, 29.17,
29.18,29.30,29.33, 32.13,
32.31, 32.32, 32.44, 32.45,
32.51, 32.53,32.59
Degenerate spirals, 35.111
Degree measure of angles, 10.2 to
10.7
Delta-(A-)definition of derivatives,
8.1 to 8.4, 8.11,8.17,8.21,
8.22, 8.24 to 8.31, 8.39, 8.45
to 8.47, 10.17, 10.44
Derivatives:
absolute value in, 9.47, 9.48,
13.34, 13.36
approximation of (see
Approximation, by
differentials)
chain rule for, 9.4 to 9.23, 9.35
to 9.44, 9.48, 9.49, 10.19 to
10.23, 10.25 to 10.29, 12.1,
12.2, 12.10, 12.29 to 12.31,
13.34, 13.36, 42.64 to 42.66,
42.68 to 42.73, 42.81 to
42.91,42.%
of definite integrals, 20.42 to
20.47,20.51,20.73, 20.74,
20.87
delta-(A-)defmition of, 8.1 to 8.4,
8.11,8.17,8.21,8.22,8.24
to 8.31, 8.39, 8.45 to 8.47,
10.17, 10.44
differentiable functions and,
8.21, 8.25, 8.26, 8.30, 8.31,
8.43 to 8.47, 9.18, 9.45,
9.49
directional, 43.1 to 43.13, 43.15
to 43.17
exponential functions, 24.7 to
24.16, 24.30 to 24.39, 24.51,
24.52, 24.64, 24.77, 24.88 to
24.90
first derivative test for relative
extrema, 13.2, 13.6 to 13.8,
13.18, 13.20, 13.29, 15.10,
15.11, 15.14, 15.15, 15.19,
15.34, 15.37, 15.44, 15.45,
15.49
generalized mean value theorem
and, 11.38, 11.39
Derivatives (Cont.):
higher-order, 12.1 to 12.13,
12.15, 12.19 to 12.23, 12.25,
12.26, 12.29 to 12.37, 12.47,
12.48, 13.1, 13.3 to 13.7,
13.20, 13.21, 39.30 to 39.32,
39.43
hyperbolic functions, 24.95,
24.96, 24.99, 24.100
implicit differentiation, 12.2,
12.11 to 12.22, 12.24, 12.34,
12.35, 12.38 to 12.48
implicit partial differentiation,
42.13 to 42.18
intermediate value theorem and,
11.28, 11.32, 11.37, 11.42
inverse trigonometric functions,
27.2, 27.4, 27.22 to 27.38,
27.58 to 27.60, 27.65, 27.69,
27.70, 27.72 to 27.79
Laplace transform of, 32.60
L'Hopital's rule and, 25.1 to
25.53, 32.4, 32.6 to 32.8,
32.20, 32.36, 36.15, 36.20,
37.47, 37.108, 38.15, 38.24,
41.56,41.57
mean value theorem and, 11.10
to 11.17, 11.30, 11.33 to
11.36, 11.38 to 11.41, 11.43,
11.45, 11.46
natural logarithms, 23.1 to 23.9
partial, 42.1 to 42.126
polynomials, 8.5, 8.6, 8.12, 8.32,
12.23
product rule for, 8.7, 8.8, 8.40,
8.41,8.48,9.10,9.16,9.40,
12.2, 12.20, 12.32
quotient rule for, 8.7, 8.9, 8.10,
8.49,8.50,9.9, 9.13,9.21,
9.38, 9.41, 9.43, 10.24, 12.1,
12.11 to 12.13, 12.19, 12.33
Rolle's theorem and, 11.1 to
11.9, 11.27, 11.31, 11.38,
11.47, 11.49
second derivative test for
relative extrema, 13.1, 13.3
to 13.7, 13.20, 13.21, 15.1 to
15.9, 15.12, 15.13, 15.16to
15.18, 15.20to 15.29, 15.32,
15.33, 15.35, 15.37, 15.39 to
15.56
sum rule for, 8.7, 9.11
trigonometric functions, 10.17 to
10.29, 10.36 to 10.43
(See also Antiderivatives)
Determinants, Hessian, 43.23
Diagonals:
cube, 14.45, 40.37, 40.38
parallelogram, 33.26, 33.30
rhombus, 33.32
Cubic functions:
as contours (level curves), 41.34
graphs of, 5.10, 5.19, 41.34
Curl, 45.28 to 45.31, 45.33, 45.34,
45.36 to 45.38
Curvature (K), 34.94 to 34.101,
34.103,35.108,35.109,45.21
to 45.23
Curves (see Graphs)
Curvilinear motion, 34.43 to
34.108
Cusps in graphs, 15.44
Cycloids:
acceleration vector for, 34.86
arch of, 34.39
curvature (K) of, 34.101
equations of, 34.20
Cylinders:
equations of, 41.26, 41.27, 41.68,
41.83,41.93,41.95,41.97
graphs of, 41.1,41.2
inscribed in cones, 16.43
surface area of, 16.22, 42.89
volume of, 14.2, 14.48, 16.7,
16.8, 16.16, 16.18, 16.43,
43.67, 44.70
Cylindrical coordinates, 41.67 to
41.85
Decay (see Exponential growth
and decay)
Decreasing functions, 11.19 to
11.26
Decreasing infinite sequences,
36.58, 36.61 to 36.63
Definite integrals:
approximating sums for, 20.1,
20.2, 20.5
convergence of, 32.1 to 32.10,
32.23 to 32.27, 32.29, 32.31,
32.41 to 32.44, 32.48, 32.53,
32.54
derivatives of, 20.42 to 20.47,
20.51, 20.73, 20.74, 20.87
exponential functions, 24.45 to
24.49, 24.55, 24.76, 24.92,
24.93,32.6,32.7,32.12to
32.14, 32.17 to 32.22, 32.38,
32.39, 32.58
inverse trigonometric functions,
27.61 to 27.64, 27.81,27.82,
32.54
Laplace transforms, 32.57 to
32.60
natural logarithms, 23.10 to
23.22, 23.53, 23.68, 23.69,
23.79, 23.80, 28.25 to 28.31,
32.4, 32.5, 32.8, 32.10,
32.15,32.16,32.36,32.37,
32.50
Definite integrals (Cont.):
powers or roots, 20.9, 20.12 to
20.14, 20.16 to 20.19, 20.23,
20.25 to 20.32, 20.35 to
20.38, 20.40, 20.57, 20.64,
20.71,20.72, 20.75 to 20.78,
20.91,20.92,23.61, 23.62
trigonometric functions, 20.10,
20.11,20.15, 20.20 to 20.22,
20.24, 20.39, 20.49, 20.60,
20.62, 20.63, 20.79 to 20.84,
28.32 to 28.34, 28.53, 29.17,
29.18,29.30,29.33, 32.13,
32.31, 32.32, 32.44, 32.45,
32.51, 32.53,32.59
Degenerate spirals, 35.111
Degree measure of angles, 10.2 to
10.7
Delta-(A-)definition of derivatives,
8.1 to 8.4, 8.11,8.17,8.21,
8.22, 8.24 to 8.31, 8.39, 8.45
to 8.47, 10.17, 10.44
Derivatives:
absolute value in, 9.47, 9.48,
13.34, 13.36
approximation of (see
Approximation, by
differentials)
chain rule for, 9.4 to 9.23, 9.35
to 9.44, 9.48, 9.49, 10.19 to
10.23, 10.25 to 10.29, 12.1,
12.2, 12.10, 12.29 to 12.31,
13.34, 13.36, 42.64 to 42.66,
42.68 to 42.73, 42.81 to
42.91,42.%
of definite integrals, 20.42 to
20.47,20.51,20.73, 20.74,
20.87
delta-(A-)defmition of, 8.1 to 8.4,
8.11,8.17,8.21,8.22,8.24
to 8.31, 8.39, 8.45 to 8.47,
10.17, 10.44
differentiable functions and,
8.21, 8.25, 8.26, 8.30, 8.31,
8.43 to 8.47, 9.18, 9.45,
9.49
directional, 43.1 to 43.13, 43.15
to 43.17
exponential functions, 24.7 to
24.16, 24.30 to 24.39, 24.51,
24.52, 24.64, 24.77, 24.88 to
24.90
first derivative test for relative
extrema, 13.2, 13.6 to 13.8,
13.18, 13.20, 13.29, 15.10,
15.11, 15.14, 15.15, 15.19,
15.34, 15.37, 15.44, 15.45,
15.49
generalized mean value theorem
and, 11.38, 11.39
Derivatives (Cont.):
higher-order, 12.1 to 12.13,
12.15, 12.19 to 12.23, 12.25,
12.26, 12.29 to 12.37, 12.47,
12.48, 13.1, 13.3 to 13.7,
13.20, 13.21, 39.30 to 39.32,
39.43
hyperbolic functions, 24.95,
24.96, 24.99, 24.100
implicit differentiation, 12.2,
12.11 to 12.22, 12.24, 12.34,
12.35, 12.38 to 12.48
implicit partial differentiation,
42.13 to 42.18
intermediate value theorem and,
11.28, 11.32, 11.37, 11.42
inverse trigonometric functions,
27.2, 27.4, 27.22 to 27.38,
27.58 to 27.60, 27.65, 27.69,
27.70, 27.72 to 27.79
Laplace transform of, 32.60
L'Hopital's rule and, 25.1 to
25.53, 32.4, 32.6 to 32.8,
32.20, 32.36, 36.15, 36.20,
37.47, 37.108, 38.15, 38.24,
41.56,41.57
mean value theorem and, 11.10
to 11.17, 11.30, 11.33 to
11.36, 11.38 to 11.41, 11.43,
11.45, 11.46
natural logarithms, 23.1 to 23.9
partial, 42.1 to 42.126
polynomials, 8.5, 8.6, 8.12, 8.32,
12.23
product rule for, 8.7, 8.8, 8.40,
8.41,8.48,9.10,9.16,9.40,
12.2, 12.20, 12.32
quotient rule for, 8.7, 8.9, 8.10,
8.49,8.50,9.9, 9.13,9.21,
9.38, 9.41, 9.43, 10.24, 12.1,
12.11 to 12.13, 12.19, 12.33
Rolle's theorem and, 11.1 to
11.9, 11.27, 11.31, 11.38,
11.47, 11.49
second derivative test for
relative extrema, 13.1, 13.3
to 13.7, 13.20, 13.21, 15.1 to
15.9, 15.12, 15.13, 15.16to
15.18, 15.20to 15.29, 15.32,
15.33, 15.35, 15.37, 15.39 to
15.56
sum rule for, 8.7, 9.11
trigonometric functions, 10.17 to
10.29, 10.36 to 10.43
(See also Antiderivatives)
Determinants, Hessian, 43.23
Diagonals:
cube, 14.45, 40.37, 40.38
parallelogram, 33.26, 33.30
rhombus, 33.32