Index
Note: Numbers following index
entries refer to problem
numbers, not page numbers.
Abel's theorem for power series,
38.60 to 38.62
Absolute extrema (see Extrema of
functions, absolute)
Absolute value:
defined, 2.24
in derivatives, 9.47, 9.48, 13.34,
13.36
in inequalities, 2.1 to 2.36
Acceleration vector, 34.51, 34.53,
34.56,34.69,34.71,34.74to
34.80, 34.83 to 34.86, 34.92,
34.106 to 34.108, 45.12, 45.16,
45.19,45.20,45.22,45.23
Addition and subtraction of
vectors, 33.2, 33.3, 33.17,
33.21, 33.22,40.30
Addition property of limits, 6.13
Alternating series test for infinite
series, 37.51, 37.59, 37.76,
37.98, 37.100,37.101,38.15
Altitudes of triangles, 3.34, 3.41,
3.73
Amplitude of trigonometric
functions, 10.13, 10.45
Angles:
between diagonals of cubes, 40.37
between diagonals and edges of
cubes, 40.38
between planes, 40.84, 40.103,
40.112
between vectors, 33.3, 33.13,
33.33, 33.35, 33.38, 33.40,
40.35, 40.37, 40.38
central, 10.1, 10.5, 10.6
degree measure of, 10.2 to 10.7
direction, 40.32
incidence, 16.52
inscribed in circles, 33.12
radian measure of, 10.1 to 10.7
reflection, 16.52
right, 33.12
(See also Trigonometric
functions)
Antiderivatives (indefinite
integrals):
exponential functions, 24.17 to
24.29,24.54,28.1 to 28.3,
28.9,28.13,28.20,28.42,
28.43, 28.50
Antiderivatives (indefinite
integrals) (Con?.):
hyperbolic functions, 24.109 to
24.111
inverse trigonometric functions,
27.39 to 27.57, 28.4, 28.21,
28.54, 29.40
natural logarithms, 23.10 to
23.22, 23.53, 23.68, 23.69,
23.79, 23.80, 28.7, 28.16,
28.19, 28.22, 28.24, 28.55 to
28.57
powers or roots, 19.1 to 19.10,
19.14, 19.17to 19.19, 19.23
to 19.30, 19.32 to 19.39,
19.41, 19.42, 19.44, 19.46,
19.49 to 19.52, 19.54, 19.57
to 19.59, 19.61 to 19.77,
19.83 to 19.97
trigonometric functions, 19.11 to
19.13, 19.15, 19.16, 19.20to
19.22, 19.31, 19.39, 19.40,
19.43, 19.45, 19.47, 19.48,
19.53, 19.55, 19.56, 19.60,
19.78 to 19.82, 19.98 to
19.100, 28.2, 28.5 to 28.12,
28.14,28.15,28.17, 28.18,
28.35 to 28.41, 28.44, 28.45,
28.49,29.1 to 29.16, 29.19 to
29.29, 29.34 to 29.37, 29.45
Approximation:
by differentials:
approximation principle statement, 18.1
cube roots, 18.4, 18.8, 18.17,
18.19, 18.21
nth power of numbers, 18.35
rational exponents, for small
numbers, 18.16
square roots, 18.2,18.3,18.20,
18.33
trigonometric functions, 18.23,
18.25, 18.26, 18.28, 18.30,
18.32
infinite series, 37.57 to 37.63,
37.65 to 37.69
of integrals:
approximation sums for definite integrals, 20.1, 20.2,
20.5
Simpson's rule for, 20.68,
20.69, 23.73
trapezoidal rule for, 20.66,
20.67, 20.70, 23.57
443
Approximation (Con?.):
natural logarithm, 38.52, 38.53,
39.28, 39.40
normal distribution, 38.46, 39.41
trigonometric function, 18.23,
18.25, 18.26, 18.28, 18.30,
18.32, 38.55, 38.75, 38.77,
39.27, 39.29
Arc length:
circular, 10.5, 10.6, 27.64, 34.32
by integration, 21.17 to 21.21,
21.30to21.34, 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
Arch of cycloids, 34.39
Archimedean spirals, 35.70, 35.76,
35.103,35.110
Area:
circle, 14.8, 14.14, 16.48
disk segment, 29.43
ellipse, 20.72, 41.22
equilateral triangle, 16.51, 16.60
by integration, 20.8, 20.15 to
20.20, 20.72, 20.88 to 20.90,
21.1 to 21.16, 21.22 to 21.29,
21.35to21.43, 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
parallelogram, 40.43, 40.110,
40.111
rectangle, 14.9, 14.34, 16.1, 16.5,
16.6, 16.15, 16.21, 16.26 to
16.29, 16.31, 16.44 to 16.46,
16.57, 16.60
right triangle, 40.36
surface (see Surface area)
Arithmetic mean, 43.51
Asymptotes, 6.28 to 6.32, 15.17 to
15.19, 15.26, 15.39to 15.43,
15.47, 15.48, 15.50, 15.52,
15.58, 15.59, 15.61
Average value of functions, 20.32,
20.33, 20.40, 20.57, 20.91
Bacterial growth, 26.2, 26.20,
26.27, 26.29, 26.37
Bernoulli's equation, 46.40 to 46.44
Bessel functions, 38.67 to 38.69
Note: Numbers following index
entries refer to problem
numbers, not page numbers.
Abel's theorem for power series,
38.60 to 38.62
Absolute extrema (see Extrema of
functions, absolute)
Absolute value:
defined, 2.24
in derivatives, 9.47, 9.48, 13.34,
13.36
in inequalities, 2.1 to 2.36
Acceleration vector, 34.51, 34.53,
34.56,34.69,34.71,34.74to
34.80, 34.83 to 34.86, 34.92,
34.106 to 34.108, 45.12, 45.16,
45.19,45.20,45.22,45.23
Addition and subtraction of
vectors, 33.2, 33.3, 33.17,
33.21, 33.22,40.30
Addition property of limits, 6.13
Alternating series test for infinite
series, 37.51, 37.59, 37.76,
37.98, 37.100,37.101,38.15
Altitudes of triangles, 3.34, 3.41,
3.73
Amplitude of trigonometric
functions, 10.13, 10.45
Angles:
between diagonals of cubes, 40.37
between diagonals and edges of
cubes, 40.38
between planes, 40.84, 40.103,
40.112
between vectors, 33.3, 33.13,
33.33, 33.35, 33.38, 33.40,
40.35, 40.37, 40.38
central, 10.1, 10.5, 10.6
degree measure of, 10.2 to 10.7
direction, 40.32
incidence, 16.52
inscribed in circles, 33.12
radian measure of, 10.1 to 10.7
reflection, 16.52
right, 33.12
(See also Trigonometric
functions)
Antiderivatives (indefinite
integrals):
exponential functions, 24.17 to
24.29,24.54,28.1 to 28.3,
28.9,28.13,28.20,28.42,
28.43, 28.50
Antiderivatives (indefinite
integrals) (Con?.):
hyperbolic functions, 24.109 to
24.111
inverse trigonometric functions,
27.39 to 27.57, 28.4, 28.21,
28.54, 29.40
natural logarithms, 23.10 to
23.22, 23.53, 23.68, 23.69,
23.79, 23.80, 28.7, 28.16,
28.19, 28.22, 28.24, 28.55 to
28.57
powers or roots, 19.1 to 19.10,
19.14, 19.17to 19.19, 19.23
to 19.30, 19.32 to 19.39,
19.41, 19.42, 19.44, 19.46,
19.49 to 19.52, 19.54, 19.57
to 19.59, 19.61 to 19.77,
19.83 to 19.97
trigonometric functions, 19.11 to
19.13, 19.15, 19.16, 19.20to
19.22, 19.31, 19.39, 19.40,
19.43, 19.45, 19.47, 19.48,
19.53, 19.55, 19.56, 19.60,
19.78 to 19.82, 19.98 to
19.100, 28.2, 28.5 to 28.12,
28.14,28.15,28.17, 28.18,
28.35 to 28.41, 28.44, 28.45,
28.49,29.1 to 29.16, 29.19 to
29.29, 29.34 to 29.37, 29.45
Approximation:
by differentials:
approximation principle statement, 18.1
cube roots, 18.4, 18.8, 18.17,
18.19, 18.21
nth power of numbers, 18.35
rational exponents, for small
numbers, 18.16
square roots, 18.2,18.3,18.20,
18.33
trigonometric functions, 18.23,
18.25, 18.26, 18.28, 18.30,
18.32
infinite series, 37.57 to 37.63,
37.65 to 37.69
of integrals:
approximation sums for definite integrals, 20.1, 20.2,
20.5
Simpson's rule for, 20.68,
20.69, 23.73
trapezoidal rule for, 20.66,
20.67, 20.70, 23.57
443
Approximation (Con?.):
natural logarithm, 38.52, 38.53,
39.28, 39.40
normal distribution, 38.46, 39.41
trigonometric function, 18.23,
18.25, 18.26, 18.28, 18.30,
18.32, 38.55, 38.75, 38.77,
39.27, 39.29
Arc length:
circular, 10.5, 10.6, 27.64, 34.32
by integration, 21.17 to 21.21,
21.30to21.34, 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
Arch of cycloids, 34.39
Archimedean spirals, 35.70, 35.76,
35.103,35.110
Area:
circle, 14.8, 14.14, 16.48
disk segment, 29.43
ellipse, 20.72, 41.22
equilateral triangle, 16.51, 16.60
by integration, 20.8, 20.15 to
20.20, 20.72, 20.88 to 20.90,
21.1 to 21.16, 21.22 to 21.29,
21.35to21.43, 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
parallelogram, 40.43, 40.110,
40.111
rectangle, 14.9, 14.34, 16.1, 16.5,
16.6, 16.15, 16.21, 16.26 to
16.29, 16.31, 16.44 to 16.46,
16.57, 16.60
right triangle, 40.36
surface (see Surface area)
Arithmetic mean, 43.51
Asymptotes, 6.28 to 6.32, 15.17 to
15.19, 15.26, 15.39to 15.43,
15.47, 15.48, 15.50, 15.52,
15.58, 15.59, 15.61
Average value of functions, 20.32,
20.33, 20.40, 20.57, 20.91
Bacterial growth, 26.2, 26.20,
26.27, 26.29, 26.37
Bernoulli's equation, 46.40 to 46.44
Bessel functions, 38.67 to 38.69