INDEX 0 449
Infinite series (Cont.):
ratio test for, 37.52, 37.53, 37.55,
37.70 to 37.72, 37.77, 37.79
to 37.81, 37.87, 37.97,
37.102,37.107,37.109, 38.1
to 38.19, 38.21, 38.22, 38.24,
38.25, 38.31, 38.33, 38.67,
38.109 to 38.113
repeating decimals as, 37.8, 37.9,
37.26
root test for, 37.91 to 37.94,
37.105,37.106,38.20,38.23
Taylor (see Taylor series)
telescoping of, 37.10
Zeno's paradox and, 37.32
Inflection points, 13.2, 13.6, 13.7,
13.18, 13.20, 14.42to 14.46,
15.2, 15.3, 15.5, 15.7, 15.8,
15.10 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
Integral test for infinite series,
37.39, 37.41,37.49,37.50,
37.53, 37.54, 37.64, 38.112
Integrals:
antiderivatives (see
Antiderivatives)
approximation of (see
Approximation, of integrals)
arc length with, 21.17 to 21.21,
21.30 to 21.34, 21.44,21.45,
23.54, 23.65, 23.66, 24.93,
27.64, 29.30 to 29.33, 34.32
to 34.42, 35.76 to 35.83
area with, 20.8, 20.15 to 20.20,
20.72, 20.88 to 20.90, 21.1 to
21.16, 21.22 to 21.29, 21.35
to 21.43, 21.46, 21.47, 23.36,
23.56, 24.45, 24.47, 24.92,
27.61, 27.62, 27.81, 27.82,
28.25,28.28, 29.43, 31.24 to
31.35,32.1, 32.33, 32.34,
32.38, 32.47, 32.55, 32.56,
35.55 to 35.71, 35.75, 44.20,
44.36 to 44.38
centroids (center of mass) with,
31.24to31.35, 35.72, 35.73,
35.88, 44.80 to 44.85, 44.89
to 44.92
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
definite (see Definite integrals)
double, 44.1 to 44.4, 44.6 to
44.46, 44.53 to 44.58, 44.74,
44.75, 44.79 to 44.82, 44.86,
44.87, 44.89, 44.90
improper, 32.1 to 32.60
Integrals (Cont.):
indefinite (see Antiderivatives)
integration by parts, 28.1 to
28.57
iterated, 44.1 to 44.5
line, 45.40 to 45.44
mass with, 44.74 to 44.79
mean-value theorem for, 20.34 to
20.37, 20.42
method of partial fractions for,
30.1 to 30.33
moments of inertia with, 44.86 to
44.88
moments with, 31.24 to 31.32,
44.80 to 44.85, 44.89 to
44.92
multiple (see Multiple integrals)
of rational functions, 30.1 to 30.33
Simpson's rule for
approximating, 20.68, 20.69,
23.73
surface area with, 31.1 to 31.15,
32.41, 35.84 to 35.86, 44.53
to 44.58
trapezoidal rule for
approximating, 20.66, 20.67,
20.70, 23.57
trigonometric substitutions in,
29.3, 29.5, 29.19 to 29.21,
29.23 to 29.27, 29.29, 29.30,
29.38 to 29.41, 29.43 to
29.45
triple, 44.5, 44.50 to 44.52, 44.59
to 44.73, 44.76 to 44.78,
44.83 to 44.85, 44.88, 44.91,
44.92
volume with, 22.1 to 22.58,
23.38, 23.59, 24.46, 24.48,
24.49, 27.63, 28.26, 28.27,
28.29 to 28.32, 29.44, 31.33
to 31.35, 32.39, 32.40,44.16
to 44.19, 44.21 to 44.23,
44.29 to 44.32, 44.34, 44.40,
44.41, 44.50, 44.51, 44.59 to
44.63, 44.66 to 44.70
work, 31.16 to 31.23, 45.43
Integrating factors for differential
equations, 46.27 to 46.33,
46.35, 46.36, 46.45
Integration by parts, 28.1 to 28.57
Intermediate value theorem, 7.20
to 7.23, 11.28, 11.32, 11.37,
11.42
Intersections:
circles, 4.24 to 4.27, 12.27
cylinders and planes, 40.18
ellipses and hyperbolas, 12.43
ellipsoids and lines, 41.20
lines, 3.44, 3.78, 3.79, 10.46,
10.47, 40.76
Intersections (Cont.):
lines and hyperbolas, 3.81
lines and parabolas, 3.80
lines and planes, 40.70
parabolas, 12.45
paraboloids and planes, 41.21
planes, 40.19, 40.85, 40.87,
40.96,40.112
in polar coordinates, 35.50 to
35.54, 35.105 to 35.107
supply and demand equations,
3.82
Inverse functions, 5.69 to 5.74,
5.92, 5.93, 5.100, 9.49
Inverse trigonometric functions:
antiderivatives (indefinite
integrals) and, 27.39 to 27.57,
28.4,28.21,28.54,29.40
definite integrals and, 27.61 to
27.64, 27.81, 27.82, 32.54
derivatives of, 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
Maclaurin series and, 39.10,
39.13, 39.31
power series for, 38.36, 38.55,
38.107, 38.115
values of, 27.5 to 27.20
Isosceles trapezoids, 3.77
Isosceles triangles, 14.46, 16.20,
16.55
Iterated integrals, 44.1 to 44.5
j unit vector, 40.28, 40.40, 40.54
k unit vector, 40.28, 40.40, 40.54
Lagrange multipliers, 43.56 to
43.64, 43.66, 43.67
Lagrange's remainder, 39.17 to
39.20, 39.22 to 39.25
Laplace transforms, 32.57 to 32.60
Laplace's equation, 42.52 to 42.54
Laplacian, 45.32
Latus rectum of parabolas, 44.80
Law of cosines, 14.33, 14.51, 33.41
Left-hand limits, 6.5, 6.33 to 6.36,
6.39
Legendre's equation, 46.80
Lemniscates, 35.32, 35.37, 35.42,
35.57, 35.85, 35.86
Length of vectors, 33.3, 33.13, 40.26
Level curves (contour maps), 41.32
to 41.43
Level surfaces, 41.44 to 41.47
L'Hopital's rule, 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
Infinite series (Cont.):
ratio test for, 37.52, 37.53, 37.55,
37.70 to 37.72, 37.77, 37.79
to 37.81, 37.87, 37.97,
37.102,37.107,37.109, 38.1
to 38.19, 38.21, 38.22, 38.24,
38.25, 38.31, 38.33, 38.67,
38.109 to 38.113
repeating decimals as, 37.8, 37.9,
37.26
root test for, 37.91 to 37.94,
37.105,37.106,38.20,38.23
Taylor (see Taylor series)
telescoping of, 37.10
Zeno's paradox and, 37.32
Inflection points, 13.2, 13.6, 13.7,
13.18, 13.20, 14.42to 14.46,
15.2, 15.3, 15.5, 15.7, 15.8,
15.10 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
Integral test for infinite series,
37.39, 37.41,37.49,37.50,
37.53, 37.54, 37.64, 38.112
Integrals:
antiderivatives (see
Antiderivatives)
approximation of (see
Approximation, of integrals)
arc length with, 21.17 to 21.21,
21.30 to 21.34, 21.44,21.45,
23.54, 23.65, 23.66, 24.93,
27.64, 29.30 to 29.33, 34.32
to 34.42, 35.76 to 35.83
area with, 20.8, 20.15 to 20.20,
20.72, 20.88 to 20.90, 21.1 to
21.16, 21.22 to 21.29, 21.35
to 21.43, 21.46, 21.47, 23.36,
23.56, 24.45, 24.47, 24.92,
27.61, 27.62, 27.81, 27.82,
28.25,28.28, 29.43, 31.24 to
31.35,32.1, 32.33, 32.34,
32.38, 32.47, 32.55, 32.56,
35.55 to 35.71, 35.75, 44.20,
44.36 to 44.38
centroids (center of mass) with,
31.24to31.35, 35.72, 35.73,
35.88, 44.80 to 44.85, 44.89
to 44.92
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
definite (see Definite integrals)
double, 44.1 to 44.4, 44.6 to
44.46, 44.53 to 44.58, 44.74,
44.75, 44.79 to 44.82, 44.86,
44.87, 44.89, 44.90
improper, 32.1 to 32.60
Integrals (Cont.):
indefinite (see Antiderivatives)
integration by parts, 28.1 to
28.57
iterated, 44.1 to 44.5
line, 45.40 to 45.44
mass with, 44.74 to 44.79
mean-value theorem for, 20.34 to
20.37, 20.42
method of partial fractions for,
30.1 to 30.33
moments of inertia with, 44.86 to
44.88
moments with, 31.24 to 31.32,
44.80 to 44.85, 44.89 to
44.92
multiple (see Multiple integrals)
of rational functions, 30.1 to 30.33
Simpson's rule for
approximating, 20.68, 20.69,
23.73
surface area with, 31.1 to 31.15,
32.41, 35.84 to 35.86, 44.53
to 44.58
trapezoidal rule for
approximating, 20.66, 20.67,
20.70, 23.57
trigonometric substitutions in,
29.3, 29.5, 29.19 to 29.21,
29.23 to 29.27, 29.29, 29.30,
29.38 to 29.41, 29.43 to
29.45
triple, 44.5, 44.50 to 44.52, 44.59
to 44.73, 44.76 to 44.78,
44.83 to 44.85, 44.88, 44.91,
44.92
volume with, 22.1 to 22.58,
23.38, 23.59, 24.46, 24.48,
24.49, 27.63, 28.26, 28.27,
28.29 to 28.32, 29.44, 31.33
to 31.35, 32.39, 32.40,44.16
to 44.19, 44.21 to 44.23,
44.29 to 44.32, 44.34, 44.40,
44.41, 44.50, 44.51, 44.59 to
44.63, 44.66 to 44.70
work, 31.16 to 31.23, 45.43
Integrating factors for differential
equations, 46.27 to 46.33,
46.35, 46.36, 46.45
Integration by parts, 28.1 to 28.57
Intermediate value theorem, 7.20
to 7.23, 11.28, 11.32, 11.37,
11.42
Intersections:
circles, 4.24 to 4.27, 12.27
cylinders and planes, 40.18
ellipses and hyperbolas, 12.43
ellipsoids and lines, 41.20
lines, 3.44, 3.78, 3.79, 10.46,
10.47, 40.76
Intersections (Cont.):
lines and hyperbolas, 3.81
lines and parabolas, 3.80
lines and planes, 40.70
parabolas, 12.45
paraboloids and planes, 41.21
planes, 40.19, 40.85, 40.87,
40.96,40.112
in polar coordinates, 35.50 to
35.54, 35.105 to 35.107
supply and demand equations,
3.82
Inverse functions, 5.69 to 5.74,
5.92, 5.93, 5.100, 9.49
Inverse trigonometric functions:
antiderivatives (indefinite
integrals) and, 27.39 to 27.57,
28.4,28.21,28.54,29.40
definite integrals and, 27.61 to
27.64, 27.81, 27.82, 32.54
derivatives of, 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
Maclaurin series and, 39.10,
39.13, 39.31
power series for, 38.36, 38.55,
38.107, 38.115
values of, 27.5 to 27.20
Isosceles trapezoids, 3.77
Isosceles triangles, 14.46, 16.20,
16.55
Iterated integrals, 44.1 to 44.5
j unit vector, 40.28, 40.40, 40.54
k unit vector, 40.28, 40.40, 40.54
Lagrange multipliers, 43.56 to
43.64, 43.66, 43.67
Lagrange's remainder, 39.17 to
39.20, 39.22 to 39.25
Laplace transforms, 32.57 to 32.60
Laplace's equation, 42.52 to 42.54
Laplacian, 45.32
Latus rectum of parabolas, 44.80
Law of cosines, 14.33, 14.51, 33.41
Left-hand limits, 6.5, 6.33 to 6.36,
6.39
Legendre's equation, 46.80
Lemniscates, 35.32, 35.37, 35.42,
35.57, 35.85, 35.86
Length of vectors, 33.3, 33.13, 40.26
Level curves (contour maps), 41.32
to 41.43
Level surfaces, 41.44 to 41.47
L'Hopital's rule, 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