448 Q INDEX
Graphs (Cont.):
ellipses, 16.20, 16.41, 34.2, 34.5,
35.16
ellipsoids, 41.13
exponential functions, 24.57 to
24.63, 24.84 to 24.86, 24.91,
24.94, 25.56, 25.57
greatest integer function, 5.6,
5.7, 6.5
hyperbolas, 5.4, 5.8, 5.9, 16.3,
34.6, 34.8, 34.15, 34.16,
41.19
hyperbolic functions, 24.97
hyperboloids, 41.14, 41.15,
41.23, 41.24
inflection points in, 13.2, 15.11
to 15.19, 15.21, 15.25, 15.26,
15.32 to 15.35, 15.37, 15.40,
15.42 to 15.46, 15.48 to
15.51, 15.53, 15.57, 15.61
inverse functions, 5.100
lemniscates, 35.32, 35.37, 35.42
limagons, 35.31, 35.38 to 35.40
line segments and lines, 3.16,
3.36,5.5,5.12, 5.14, 5.15 to
5.18,5.20,5.23,5.88,6.33,
7.2, 7.4, 7.5, 7.8, 8.43,
10.46, 11.49, 16.45, 34.9,
34.10, 35.10 to 35.12, 35.19,
35.20, 40.21
natural logarithms, 23.39, 23.40,
23.46, 23.47, 23.55, 23.76,
25.54, 25.55
one-one functions, 5.100
parabolas, 5.1,5.2, 5.11,5.101,
8.44, 15.30, 16.2, 16.47,
34.3, 34.4,34.7, 35.15,41.19
paraboloids, 41.4, 41.5, 41.9,
41.17,41.25
planes, 40.87, 41.3, 41.18
point functions, 5.13
relative extrema in, 13.1, 13.2,
15.11 to 15.15, 15.17to
15.19, 15.22to 15.24, 15.31
to 15.35, 15.39, 15.41 to
15.46, 15.48 to 15.51, 15.53,
15.54, 15.57, 15.61
roses, 35.33, 35.47, 35.48, 35.93
saddle surfaces, 41.19
spheres, 41.31
tractrix, 29.42
trigonometric functions, 10.11 to
10.13, 15.32 to 15.38, 15.51,
15.53, 27.1, 27.3, 27.71
Gravity, 19.95, 19.96
Greatest integer function, 5.6, 5.7,
6.5
Green's theorem, 45.47 to 45.49
Growth (see Exponential growth
and decay)
Half-life of radioactive materials,
26.15 to 26.18, 26.21,26.30,
26.43
Harmonic series, 37.2, 37.3, 37.27,
37.28, 38.6
Hessian determinant, 43.23
Higher-order derivatives, 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
Homogeneous multivariate
functions, 42.74 to 42.80
Hooke'slaw, 31.16, 31.17
Hyperbolas:
as contours (level curves), 41.36,
41.40
curvature (K) of, 34.99
equations of, 41.11
graphs of, 5.4, 5.8, 5.9, 16.3, 34.6,
34.8,34.15,34.16,41.19
intersections of ellipses with,
12.43
intersections of lines with, 3.81
parametric equations of, 34.6,
34.8, 34.12,34.15, 34.16
Hyperbolic functions:
antiderivatives (indefinite
integrals) and, 24.109 to
24.111
derivatives of, 24.95, 24.96,
24.99, 24.100
graphs of, 24.97
identities for, 24.98, 24.101 to
24.108
Maclaurin series and, 39.14
power series and, 38.43, 38.44,
38.95
Hyperboloids:
equations of, 41.7
graphs of, 41.14, 41.15, 41.23,
41.24
as level surfaces, 41.46
as ruled surfaces, 41.29
Hypergeometric series, 38.113,
38.115
i unit vector, 40.28, 40.40, 40.54
Ideal gas law, 42.23
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
Improper integrals, 32.1 to 32.60
Increasing functions, 11.18, 11.20
to 11.26, 11.29, 11.48, 15.52
Increasing infinite sequences, 36.54
to 36.57, 36.59, 36.60
Indefinite integrals (see
Antiderivatives)
Induction, mathematical, 2.18,
20.3, 20.65, 24.89, 24.90,
32.22, 43.20
Inequalities:
absolute value in, 2.1 to 2.36
Cauchy's, 33.28, 33.29, 43.68
introduced, 1.1 to 1.25
for natural logarithms, 23.41,
23.42, 23.60, 23.77
triangle, 2.18, 2.19, 2.35, 6.13,
33.29, 36.47, 36.49 to 36.51
Inertia, moments of, 44.86 to
44.88
Infinite sequences:
bounded, 36.47, 36.62
convergence of, 36.19 to 36.45,
36.47, 36.52, 36.62
decreasing, 36.58, 36.61 to 36.63
increasing, 36.54 to 36.57, 36.59,
36.60
limits of, 36.1 to 36.53, 36.65
Infinite series:
alternating series test for, 37.51,
37.59, 37.76, 37.98, 37.100,
37.101,38.15
approximation of, 37.57 to 37.63,
37.65 to 37.69
binomial series, 38.31, 38.78,
38.103 to 38.106, 38.108
convergence of, 37.1 to 37.3,
37.5, 37.10 to 37.16, 37.23,
37.24, 37.27 to 37.56, 37.64,
37.69 to 37.116
for Euler's constant (y), 37.110
geometric series, 37.5 to 37.9,
37.12,37.13,37.25,37.26,
37.30 to 37.34, 37.45, 37.48,
37.67, 37.68, 37.73, 37.75,
37.77,37.83, 37.91, 37.113
to 37.116, 38.5, 38.26,38.29
harmonic series, 37.2, 37.3,
37.27, 37.28, 38.6
integral test for, 37.39, 37.41,
37.49, 37.50, 37.53, 37.54,
37.64,38.112
limit comparison test for, 37.42
to 37.47, 37.54, 37.76, 37.78,
37.82, 37.84, 37.86, 37.88 to
37.90, 37.96, 37.98, 37.100,
37.101, 37.108
Maclaurin (see Maclaurin series)
p-series, 37.40, 37.44, 37.47,
37.54, 37.69, 37.74, 37.78,
37.82, 37.85, 37.88, 37.89,
37.95,38.11,38.21
partial sums of, 37.4, 37.5, 37.10,
37.17 to 37.22, 37.24, 37.25
power (see Power series)
Graphs (Cont.):
ellipses, 16.20, 16.41, 34.2, 34.5,
35.16
ellipsoids, 41.13
exponential functions, 24.57 to
24.63, 24.84 to 24.86, 24.91,
24.94, 25.56, 25.57
greatest integer function, 5.6,
5.7, 6.5
hyperbolas, 5.4, 5.8, 5.9, 16.3,
34.6, 34.8, 34.15, 34.16,
41.19
hyperbolic functions, 24.97
hyperboloids, 41.14, 41.15,
41.23, 41.24
inflection points in, 13.2, 15.11
to 15.19, 15.21, 15.25, 15.26,
15.32 to 15.35, 15.37, 15.40,
15.42 to 15.46, 15.48 to
15.51, 15.53, 15.57, 15.61
inverse functions, 5.100
lemniscates, 35.32, 35.37, 35.42
limagons, 35.31, 35.38 to 35.40
line segments and lines, 3.16,
3.36,5.5,5.12, 5.14, 5.15 to
5.18,5.20,5.23,5.88,6.33,
7.2, 7.4, 7.5, 7.8, 8.43,
10.46, 11.49, 16.45, 34.9,
34.10, 35.10 to 35.12, 35.19,
35.20, 40.21
natural logarithms, 23.39, 23.40,
23.46, 23.47, 23.55, 23.76,
25.54, 25.55
one-one functions, 5.100
parabolas, 5.1,5.2, 5.11,5.101,
8.44, 15.30, 16.2, 16.47,
34.3, 34.4,34.7, 35.15,41.19
paraboloids, 41.4, 41.5, 41.9,
41.17,41.25
planes, 40.87, 41.3, 41.18
point functions, 5.13
relative extrema in, 13.1, 13.2,
15.11 to 15.15, 15.17to
15.19, 15.22to 15.24, 15.31
to 15.35, 15.39, 15.41 to
15.46, 15.48 to 15.51, 15.53,
15.54, 15.57, 15.61
roses, 35.33, 35.47, 35.48, 35.93
saddle surfaces, 41.19
spheres, 41.31
tractrix, 29.42
trigonometric functions, 10.11 to
10.13, 15.32 to 15.38, 15.51,
15.53, 27.1, 27.3, 27.71
Gravity, 19.95, 19.96
Greatest integer function, 5.6, 5.7,
6.5
Green's theorem, 45.47 to 45.49
Growth (see Exponential growth
and decay)
Half-life of radioactive materials,
26.15 to 26.18, 26.21,26.30,
26.43
Harmonic series, 37.2, 37.3, 37.27,
37.28, 38.6
Hessian determinant, 43.23
Higher-order derivatives, 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
Homogeneous multivariate
functions, 42.74 to 42.80
Hooke'slaw, 31.16, 31.17
Hyperbolas:
as contours (level curves), 41.36,
41.40
curvature (K) of, 34.99
equations of, 41.11
graphs of, 5.4, 5.8, 5.9, 16.3, 34.6,
34.8,34.15,34.16,41.19
intersections of ellipses with,
12.43
intersections of lines with, 3.81
parametric equations of, 34.6,
34.8, 34.12,34.15, 34.16
Hyperbolic functions:
antiderivatives (indefinite
integrals) and, 24.109 to
24.111
derivatives of, 24.95, 24.96,
24.99, 24.100
graphs of, 24.97
identities for, 24.98, 24.101 to
24.108
Maclaurin series and, 39.14
power series and, 38.43, 38.44,
38.95
Hyperboloids:
equations of, 41.7
graphs of, 41.14, 41.15, 41.23,
41.24
as level surfaces, 41.46
as ruled surfaces, 41.29
Hypergeometric series, 38.113,
38.115
i unit vector, 40.28, 40.40, 40.54
Ideal gas law, 42.23
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
Improper integrals, 32.1 to 32.60
Increasing functions, 11.18, 11.20
to 11.26, 11.29, 11.48, 15.52
Increasing infinite sequences, 36.54
to 36.57, 36.59, 36.60
Indefinite integrals (see
Antiderivatives)
Induction, mathematical, 2.18,
20.3, 20.65, 24.89, 24.90,
32.22, 43.20
Inequalities:
absolute value in, 2.1 to 2.36
Cauchy's, 33.28, 33.29, 43.68
introduced, 1.1 to 1.25
for natural logarithms, 23.41,
23.42, 23.60, 23.77
triangle, 2.18, 2.19, 2.35, 6.13,
33.29, 36.47, 36.49 to 36.51
Inertia, moments of, 44.86 to
44.88
Infinite sequences:
bounded, 36.47, 36.62
convergence of, 36.19 to 36.45,
36.47, 36.52, 36.62
decreasing, 36.58, 36.61 to 36.63
increasing, 36.54 to 36.57, 36.59,
36.60
limits of, 36.1 to 36.53, 36.65
Infinite series:
alternating series test for, 37.51,
37.59, 37.76, 37.98, 37.100,
37.101,38.15
approximation of, 37.57 to 37.63,
37.65 to 37.69
binomial series, 38.31, 38.78,
38.103 to 38.106, 38.108
convergence of, 37.1 to 37.3,
37.5, 37.10 to 37.16, 37.23,
37.24, 37.27 to 37.56, 37.64,
37.69 to 37.116
for Euler's constant (y), 37.110
geometric series, 37.5 to 37.9,
37.12,37.13,37.25,37.26,
37.30 to 37.34, 37.45, 37.48,
37.67, 37.68, 37.73, 37.75,
37.77,37.83, 37.91, 37.113
to 37.116, 38.5, 38.26,38.29
harmonic series, 37.2, 37.3,
37.27, 37.28, 38.6
integral test for, 37.39, 37.41,
37.49, 37.50, 37.53, 37.54,
37.64,38.112
limit comparison test for, 37.42
to 37.47, 37.54, 37.76, 37.78,
37.82, 37.84, 37.86, 37.88 to
37.90, 37.96, 37.98, 37.100,
37.101, 37.108
Maclaurin (see Maclaurin series)
p-series, 37.40, 37.44, 37.47,
37.54, 37.69, 37.74, 37.78,
37.82, 37.85, 37.88, 37.89,
37.95,38.11,38.21
partial sums of, 37.4, 37.5, 37.10,
37.17 to 37.22, 37.24, 37.25
power (see Power series)