444
INDEX
Bessel's equation, 38.70, 38.71,
46.81
Binomial series, 38.31, 38.78,
38.103 to 38.106, 38.108
Binormal vectors, 45.17
Bounded infinite sequences, 36.47,
36.62
Boyle's law, 14.39
Cardioids, 35.30, 35.34 to 35.36,
35.44, 35.49, 35.55, 35.66,
35.67, 35.69, 35.73, 35.78,
35.84, 35.91, 35.102,44.33,
44.38, 44.81
Cartesian coordinates (see
Rectangular coordinates)
Cauchy-Riemann equations, 42.54,
42.92
Cauchy's inequality, 33.28, 33.29,
43.68
Celsius temperature scale, 3.71
Center of circles, 4.1 to 4.6, 4.10
to 4.15, 4.23
Center of mass (see Centroids)
Central angles, 10.1, 10.5, 10.6
Centroids (center of mass):
by integration, 31.24 to 31.35,
35.72, 35.73, 35.88, 44.80 to
44.85, 44.89 to 44.92
right triangle, 31.28, 31.34
Chain rule:
for derivatives, 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, 12.29to 12.31,
13.34, 13.36, 42.64 to 42.66,
42.68 to 42.73, 42.81 to
42.91, 42.96
for vector functions, 34.61
Circles:
angles inscribed in, 33.12
arc length and, 10.5, 10.6, 27.64,
34.32
area of, 14.8, 14.14, 16.48
center of, 4.1 to 4.6, 4.10 to
4.15,4.23
circumference of, 27.64, 34.32
as contours (level curves), 41.32
curvilinear motion and, 34.74 to
34.76
equations of, 4.1 to 4.6, 4.9,
4.10,4.12,4.13,4.17to
4.20, 4.22, 4.25 to 4.30
graphs of, 5.3, 34.1, 35.7 to 35.9,
35.13, 35.14,35.17, 35.18,
35.41, 35.66, 35.67, 35.69,
35.87, 44.33, 44.37, 44.38,
44.42, 44.44
intersections of, 4.24 to 4.27,
12.27
Circles (Cont.):
parametric equations of, 34.1,
34.17
perimeter of, 16.46
in polar coordinates, 35.7 to
35.9,35.13, 35.14, 35.17,
35.18, 35.41, 35.66 to 35.69,
35.87, 35.88, 44.33, 44.38,
44.42, 44.44
radius of, 4.1 to 4.6, 4.10 to
4.15,4.23
tangents to, 4.15, 4.19 to 4.22,
12.46
triangles inscribed in, 16.61
Circumference of circles, 27.64,
34.32
Collinear points, 40.15
Completing the square, 4.6 to 4.8,
4.10,4.11,4.13, 4.16, 27.51,
27.53, 29.29, 29.39, 30.13,
34.14,40.11
Components of vectors, 33.4, 33.5
Composite functions, 9.1 to 9.6,
9.24 to 9.34, 9.46, 10.19
Compound interest, 26.8 to 26.14,
26.40 to 26.42
Concave functions, 15.1 to 15.5,
15.16, 15.17, 15.20, 15.21,
15.23 to 15.29, 15.39 to
15.41, 15.43, 15.44, 15.48,
15.52, 34.29, 34.30
Cones:
circumscribed about spheres,
16.42
cylinders inscribed in, 16.43
equations of, 41.75, 41.77, 41.87
frustrum of, 22.49
graphs of, 41.8, 41.10,41.16
surface area of, 16.9, 31.14,
44.58
volume of, 14.6, 14.18, 14.29,
14.38, 16.9, 16.42, 22.2,
31.34,42.86,43.67,44.41,
44.51
Continuity of functions:
composite functions, 9.46
definite integrals, 20.42, 20.59
differentiable functions, 8.25,
8.26
generalized mean value theorem
and, 11.38, 11.39
intermediate value theorem and,
7.20 to 7.23, 11.28, 11.32,
11.37, 11.42
over an interval, 7.24 to 7.27
on the left, 7.18, 7.19
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
Continuity of functions (Cont.):
multivariate functions, 41.60 to
41.63
at a point, 7.1 to 7.23, 9.46
removable discontinuities, 7.5,
7.9
on the right, 7.18, 7.19
Rolle's theorem and, 11.1 to
11.9, 11.27, 11.31, 11.38,
11.47, 11.49
Contour maps (level curves), 41.32
to 41.43
Convergence:
infinite sequences, 36.19 to
36.45, 36.47, 36.52, 36.62
infinite series, 37.1 to 37.3, 37.5,
37.10to37.16, 37.23, 37.24,
37.27 to 37.56, 37.64, 37.69
to 37.116
integrals, 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
power series, 38.1 to 38.33,
38.67, 38.68,38.109to
38.114
vector, 34.43
Coordinate systems:
Cartesian (see Rectangular
coordinates)
cylindrical, 41.67 to 41.85
polar (see Polar coordinates)
rectangular (see Rectangular
coordinates)
spherical, 41.85 to 41.98
Coulomb's law, 31.22
Critical numbers:
absolute extrema and, 13.9 to
13.13, 13.15to 13.17, 13.21,
13.23 to 13.34, 13.36, 15.31
relative extrema and, 13.3 to
13.8, 13.14, 13.18to 13.20,
15.6 to 15.15, 15.17 to 15.22,
15.31 to 15.35, 15.39, 15.41
to 15.46, 15.48to 15.51,
15.53, 15.54
Cross product of vectors, 40.40 to
40.43, 40.45 to 40.68, 45.11,
45.12, 45.17 to 45.20, 45.22,
45.23, 45.28, 45.36, 45.37,
45.39
Cube roots:
approximation of, 18.4, 18.8,
18.17, 18.19, 18.21
in limits, 6.50, 6.51
of real numbers, 5.84
Cubes:
diagonals of, 14.45, 40.37,
40.38
difference of, 5.84
edges of, 40.38
INDEX
Bessel's equation, 38.70, 38.71,
46.81
Binomial series, 38.31, 38.78,
38.103 to 38.106, 38.108
Binormal vectors, 45.17
Bounded infinite sequences, 36.47,
36.62
Boyle's law, 14.39
Cardioids, 35.30, 35.34 to 35.36,
35.44, 35.49, 35.55, 35.66,
35.67, 35.69, 35.73, 35.78,
35.84, 35.91, 35.102,44.33,
44.38, 44.81
Cartesian coordinates (see
Rectangular coordinates)
Cauchy-Riemann equations, 42.54,
42.92
Cauchy's inequality, 33.28, 33.29,
43.68
Celsius temperature scale, 3.71
Center of circles, 4.1 to 4.6, 4.10
to 4.15, 4.23
Center of mass (see Centroids)
Central angles, 10.1, 10.5, 10.6
Centroids (center of mass):
by integration, 31.24 to 31.35,
35.72, 35.73, 35.88, 44.80 to
44.85, 44.89 to 44.92
right triangle, 31.28, 31.34
Chain rule:
for derivatives, 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, 12.29to 12.31,
13.34, 13.36, 42.64 to 42.66,
42.68 to 42.73, 42.81 to
42.91, 42.96
for vector functions, 34.61
Circles:
angles inscribed in, 33.12
arc length and, 10.5, 10.6, 27.64,
34.32
area of, 14.8, 14.14, 16.48
center of, 4.1 to 4.6, 4.10 to
4.15,4.23
circumference of, 27.64, 34.32
as contours (level curves), 41.32
curvilinear motion and, 34.74 to
34.76
equations of, 4.1 to 4.6, 4.9,
4.10,4.12,4.13,4.17to
4.20, 4.22, 4.25 to 4.30
graphs of, 5.3, 34.1, 35.7 to 35.9,
35.13, 35.14,35.17, 35.18,
35.41, 35.66, 35.67, 35.69,
35.87, 44.33, 44.37, 44.38,
44.42, 44.44
intersections of, 4.24 to 4.27,
12.27
Circles (Cont.):
parametric equations of, 34.1,
34.17
perimeter of, 16.46
in polar coordinates, 35.7 to
35.9,35.13, 35.14, 35.17,
35.18, 35.41, 35.66 to 35.69,
35.87, 35.88, 44.33, 44.38,
44.42, 44.44
radius of, 4.1 to 4.6, 4.10 to
4.15,4.23
tangents to, 4.15, 4.19 to 4.22,
12.46
triangles inscribed in, 16.61
Circumference of circles, 27.64,
34.32
Collinear points, 40.15
Completing the square, 4.6 to 4.8,
4.10,4.11,4.13, 4.16, 27.51,
27.53, 29.29, 29.39, 30.13,
34.14,40.11
Components of vectors, 33.4, 33.5
Composite functions, 9.1 to 9.6,
9.24 to 9.34, 9.46, 10.19
Compound interest, 26.8 to 26.14,
26.40 to 26.42
Concave functions, 15.1 to 15.5,
15.16, 15.17, 15.20, 15.21,
15.23 to 15.29, 15.39 to
15.41, 15.43, 15.44, 15.48,
15.52, 34.29, 34.30
Cones:
circumscribed about spheres,
16.42
cylinders inscribed in, 16.43
equations of, 41.75, 41.77, 41.87
frustrum of, 22.49
graphs of, 41.8, 41.10,41.16
surface area of, 16.9, 31.14,
44.58
volume of, 14.6, 14.18, 14.29,
14.38, 16.9, 16.42, 22.2,
31.34,42.86,43.67,44.41,
44.51
Continuity of functions:
composite functions, 9.46
definite integrals, 20.42, 20.59
differentiable functions, 8.25,
8.26
generalized mean value theorem
and, 11.38, 11.39
intermediate value theorem and,
7.20 to 7.23, 11.28, 11.32,
11.37, 11.42
over an interval, 7.24 to 7.27
on the left, 7.18, 7.19
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
Continuity of functions (Cont.):
multivariate functions, 41.60 to
41.63
at a point, 7.1 to 7.23, 9.46
removable discontinuities, 7.5,
7.9
on the right, 7.18, 7.19
Rolle's theorem and, 11.1 to
11.9, 11.27, 11.31, 11.38,
11.47, 11.49
Contour maps (level curves), 41.32
to 41.43
Convergence:
infinite sequences, 36.19 to
36.45, 36.47, 36.52, 36.62
infinite series, 37.1 to 37.3, 37.5,
37.10to37.16, 37.23, 37.24,
37.27 to 37.56, 37.64, 37.69
to 37.116
integrals, 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
power series, 38.1 to 38.33,
38.67, 38.68,38.109to
38.114
vector, 34.43
Coordinate systems:
Cartesian (see Rectangular
coordinates)
cylindrical, 41.67 to 41.85
polar (see Polar coordinates)
rectangular (see Rectangular
coordinates)
spherical, 41.85 to 41.98
Coulomb's law, 31.22
Critical numbers:
absolute extrema and, 13.9 to
13.13, 13.15to 13.17, 13.21,
13.23 to 13.34, 13.36, 15.31
relative extrema and, 13.3 to
13.8, 13.14, 13.18to 13.20,
15.6 to 15.15, 15.17 to 15.22,
15.31 to 15.35, 15.39, 15.41
to 15.46, 15.48to 15.51,
15.53, 15.54
Cross product of vectors, 40.40 to
40.43, 40.45 to 40.68, 45.11,
45.12, 45.17 to 45.20, 45.22,
45.23, 45.28, 45.36, 45.37,
45.39
Cube roots:
approximation of, 18.4, 18.8,
18.17, 18.19, 18.21
in limits, 6.50, 6.51
of real numbers, 5.84
Cubes:
diagonals of, 14.45, 40.37,
40.38
difference of, 5.84
edges of, 40.38