452 Q INDEX
Perpendicular vectors, 33.4 to 33.8,
33.12, 33.18,33.19,33.21,
33.31, 33.32, 33.37, 33.39,
40.36, 40.39, 40.41, 40.42,
40.51, 40.68
Planes:
angle between, 40.84, 40.103,
40.112
cut by lines, 40.99 to 40.102,
40.104,40.105
distance between, 40.91, 40.92
distances from points to, 40.88,
40.89
equations of, 40.80 to 40.83,
40.86,40.93,40.98,41.69,
41.78,41.82,41.96
graphs of, 40.87, 41.3, 41.18
intersections of, 40.19, 40.85,
40.87,40.96,40.112
as level surfaces, 41.44
normal, 42.120, 42.121, 45.3,
45.4, 45.6
osculating, 45.18 to 45.20
parallel, 40.90, 40.91
perpendicular, 40.95
tangent, 40.94, 42.31, 42.105 to
42.115, 42.122 to 42.126
vectors and, 40.106 to 40.108
Plots (see Graphs)
Point-slope equations of lines, 3.2,
3.48 to 3.51, 10.22, 10.23,
10.25, 10.28
Polar coordinates:
arc length calculations in, 35.76
to 35.83
area calculations in, 35.55 to
35.71, 35.75
cardioids in, 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
centroid calculations in, 35.72,
35.73, 35.88
circles in, 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
curvature (K) in, 35.108,
35.109
ellipses in, 35.16
intersections in, 35.50 to 35.54,
35.105 to 35.107
lemniscates in, 35.32, 35.37,
35.42, 35.57, 35.85, 35.86
limacons in, 35.31, 35.38 to
35.40, 35.56, 35.59, 35.60
lines in, 35.10 to 35.12, 35.19,
35.20
parabolas in, 35.15
Polar coordinates (Cont.):
polar-to-rectangular
transformations, 35.1, 35.4
to 35.6, 41.67
rectangular-to-polar
transformations, 35.1 to
35.3,35.21 to 35.27, 41.67
roses (curves) in, 35.33, 35.47,
35.48, 35.58, 35.64, 35.65,
35.72, 35.93
slope in, 35.93, 35.94, 35.96,
35.97
surface area calculations in,
35.84 to 35.86
Polynomials:
derivatives of, 8.5, 8.6, 8.12,
8.32, 12.23
factorization of, 5.76 to 5.86
limits of, 6.2 to 6.4, 6.6 to 6.8,
6.10,6.11,6.12,6.14to
6.16, 6.17 to 6.19, 6.20 to
6.22, 6.28, 6.32, 6.37, 6.42,
6.43 to 6.49
roots of, 5.76 to 5.82, 11.28
Population growth, 26.5, 26.7,
26.19, 26.25, 26.26, 26.28,
26.38
Position vector, 34.44 to 34.56,
34.59, 34.60, 34.65 to 34.72,
34.74 to 34.81,34.82 to
34.96,34.100,34.101,
34.103, 34.105 to 34.108,
45.1,45.2, 45.4 to 45.6,
45.12, 45.15 to 45.23
Power series:
Abel's theorem for, 38.60 to
38.62
Bessel functions, 38.67 to 38.69
convergence of, 38.1 to 38.33,
38.67, 38.68, 38.109 to
38.114
differential equation solutions
with, 38.49, 38.56, 38.66
exponential functions and, 38.39
to 38.42, 38.76, 38.78 to
38.80, 38.82, 38.97
hyperbolic functions and, 38.43,
38.44, 38.95
hypergeometric series, 38.113,
38.115
inverse trigonometric functions
and, 38.36, 38.55,38.107,
38.115
natural logarithms and, 38.38,
38.50 to 38.53, 38.60, 38.86,
38.88, 38.94, 38.99, 38.100
normal distribution, 38.45
powers or roots, 38.34, 38.35,
38.37, 38.64, 38.65, 38.72,
38.105, 38.106, 38.108
Power series (Cont.):
trigonometric functions and,
38.58, 38.59, 38.63, 38.75 to
38,77, 38.79 to 38.83, 38.86,
38.89 to 38.91, 38.96
Predator-prey system, 46.70
Principal unit normal vector, 34.81
to 34.86, 34.88,34.90, 34.91,
34.105 to 34.107, 45.16
Product rule:
for derivatives, 8.7, 8.8, 8.40,
8.41, 8.48, 9.10, 9.16, 9.40,
12.2, 12.20, 12.32
for limits, 36.50
for vector functions, 34.54,
34.57, 34.73, 34.92
Pyramids, 22.22
Pythagorean theorem, 4.21, 14.1,
14.5, 40.34
Quadratic equations, discriminant
for, 30.13, 46.48
Quadrilaterals, 3.42
Quotient rule:
for derivatives, 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
for vector functions, 34.73
Radian measure of angles, 10.1 to
10.7
Radioactive decay, 26.15 to 26.18,
26.21, 26.30, 26.43
Radius of circles, 4.1 to 4.6, 4.10
to 4.15, 4.23
Radius of curvature (-rho-), 34.94,
34.95, 34.102, 34.104, 34.105
Range of functions, 5.1 to 5.19, 5.24
to 5.31, 5.34 to 5.37, 27.21
Rates, related, 14.1 to 14.56
Ratio test for infinite series, 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
Rational function integration, 30.1
to 30.33
Rectangles:
area of, 14.9, 14.34, 16.1, 16.5,
16.6, 16.15, 16.21, 16.26to
16.29, 16.31, 16.44to 16.46,
16.57, 16.60
inscribed in ellipses, 16.41
perimeter of, 16.1, 16.15, 16.29,
16.35, 16.41, 16.44, 16.46,
16.60
Perpendicular vectors, 33.4 to 33.8,
33.12, 33.18,33.19,33.21,
33.31, 33.32, 33.37, 33.39,
40.36, 40.39, 40.41, 40.42,
40.51, 40.68
Planes:
angle between, 40.84, 40.103,
40.112
cut by lines, 40.99 to 40.102,
40.104,40.105
distance between, 40.91, 40.92
distances from points to, 40.88,
40.89
equations of, 40.80 to 40.83,
40.86,40.93,40.98,41.69,
41.78,41.82,41.96
graphs of, 40.87, 41.3, 41.18
intersections of, 40.19, 40.85,
40.87,40.96,40.112
as level surfaces, 41.44
normal, 42.120, 42.121, 45.3,
45.4, 45.6
osculating, 45.18 to 45.20
parallel, 40.90, 40.91
perpendicular, 40.95
tangent, 40.94, 42.31, 42.105 to
42.115, 42.122 to 42.126
vectors and, 40.106 to 40.108
Plots (see Graphs)
Point-slope equations of lines, 3.2,
3.48 to 3.51, 10.22, 10.23,
10.25, 10.28
Polar coordinates:
arc length calculations in, 35.76
to 35.83
area calculations in, 35.55 to
35.71, 35.75
cardioids in, 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
centroid calculations in, 35.72,
35.73, 35.88
circles in, 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
curvature (K) in, 35.108,
35.109
ellipses in, 35.16
intersections in, 35.50 to 35.54,
35.105 to 35.107
lemniscates in, 35.32, 35.37,
35.42, 35.57, 35.85, 35.86
limacons in, 35.31, 35.38 to
35.40, 35.56, 35.59, 35.60
lines in, 35.10 to 35.12, 35.19,
35.20
parabolas in, 35.15
Polar coordinates (Cont.):
polar-to-rectangular
transformations, 35.1, 35.4
to 35.6, 41.67
rectangular-to-polar
transformations, 35.1 to
35.3,35.21 to 35.27, 41.67
roses (curves) in, 35.33, 35.47,
35.48, 35.58, 35.64, 35.65,
35.72, 35.93
slope in, 35.93, 35.94, 35.96,
35.97
surface area calculations in,
35.84 to 35.86
Polynomials:
derivatives of, 8.5, 8.6, 8.12,
8.32, 12.23
factorization of, 5.76 to 5.86
limits of, 6.2 to 6.4, 6.6 to 6.8,
6.10,6.11,6.12,6.14to
6.16, 6.17 to 6.19, 6.20 to
6.22, 6.28, 6.32, 6.37, 6.42,
6.43 to 6.49
roots of, 5.76 to 5.82, 11.28
Population growth, 26.5, 26.7,
26.19, 26.25, 26.26, 26.28,
26.38
Position vector, 34.44 to 34.56,
34.59, 34.60, 34.65 to 34.72,
34.74 to 34.81,34.82 to
34.96,34.100,34.101,
34.103, 34.105 to 34.108,
45.1,45.2, 45.4 to 45.6,
45.12, 45.15 to 45.23
Power series:
Abel's theorem for, 38.60 to
38.62
Bessel functions, 38.67 to 38.69
convergence of, 38.1 to 38.33,
38.67, 38.68, 38.109 to
38.114
differential equation solutions
with, 38.49, 38.56, 38.66
exponential functions and, 38.39
to 38.42, 38.76, 38.78 to
38.80, 38.82, 38.97
hyperbolic functions and, 38.43,
38.44, 38.95
hypergeometric series, 38.113,
38.115
inverse trigonometric functions
and, 38.36, 38.55,38.107,
38.115
natural logarithms and, 38.38,
38.50 to 38.53, 38.60, 38.86,
38.88, 38.94, 38.99, 38.100
normal distribution, 38.45
powers or roots, 38.34, 38.35,
38.37, 38.64, 38.65, 38.72,
38.105, 38.106, 38.108
Power series (Cont.):
trigonometric functions and,
38.58, 38.59, 38.63, 38.75 to
38,77, 38.79 to 38.83, 38.86,
38.89 to 38.91, 38.96
Predator-prey system, 46.70
Principal unit normal vector, 34.81
to 34.86, 34.88,34.90, 34.91,
34.105 to 34.107, 45.16
Product rule:
for derivatives, 8.7, 8.8, 8.40,
8.41, 8.48, 9.10, 9.16, 9.40,
12.2, 12.20, 12.32
for limits, 36.50
for vector functions, 34.54,
34.57, 34.73, 34.92
Pyramids, 22.22
Pythagorean theorem, 4.21, 14.1,
14.5, 40.34
Quadratic equations, discriminant
for, 30.13, 46.48
Quadrilaterals, 3.42
Quotient rule:
for derivatives, 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
for vector functions, 34.73
Radian measure of angles, 10.1 to
10.7
Radioactive decay, 26.15 to 26.18,
26.21, 26.30, 26.43
Radius of circles, 4.1 to 4.6, 4.10
to 4.15, 4.23
Radius of curvature (-rho-), 34.94,
34.95, 34.102, 34.104, 34.105
Range of functions, 5.1 to 5.19, 5.24
to 5.31, 5.34 to 5.37, 27.21
Rates, related, 14.1 to 14.56
Ratio test for infinite series, 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
Rational function integration, 30.1
to 30.33
Rectangles:
area of, 14.9, 14.34, 16.1, 16.5,
16.6, 16.15, 16.21, 16.26to
16.29, 16.31, 16.44to 16.46,
16.57, 16.60
inscribed in ellipses, 16.41
perimeter of, 16.1, 16.15, 16.29,
16.35, 16.41, 16.44, 16.46,
16.60