INDEX 0 453
Rectangular coordinates:
cylindrical coordinates and,
41.67, 41.70 to 41.74, 41.80
to 41.85
cylindrical-to-rectangular
transformations, 41.67
polar-to-rectangular
transformations, 35.1, 35.4
to 35.6, 41.67
rectangular-to-cylindrical
transformations, 41.67
rectangular-to-polar
transformations, 35.1 to
35.3, 35.21 to 35.27, 41.67
rectangular-to-spherical
transformations, 41.85
spherical coordinates and, 41.85,
41.88 to 41.93
spherical-to-rectangular
transformations, 41.85
Rectangular form of vectors, 33.14
to 33.16
Rectilinear motion, 17.1 to 17.35,
19.34 to 19.39, 19.41, 19.44,
19.57, 19.59, 19.72 to 19.76
Reflections of curves and lines,
5.94 to 5.100
Related rates, 14.1 to 14.56
Relative extrema (see Extrema of
functions, relative)
Removable discontinuities, 7.5, 7.9
Repeating decimals as infinite
series, 37.8, 37.9, 37.26
Revolution:
surface of, 41.4 to 41.12
volume of, 31.33 to 31.35
Rhombuses:
diagonals of, 33.32
as parallelograms, 3.76
Riccati equation, 46.43, 46.44
Right angles, 33.12
Right-hand limits, 6.5, 6.33 to 6.36,
6.39
Right triangles:
area of, 40.36
centroidof, 31.28, 31.34
perimeter of, 16.19
Pythagorean theorem for, 4.21,
14.1, 14.5,40.34
vertices of, 3.25, 3.26, 40.13
Rolle's theorem, 11.1 to 11.9,
11.27, 11.31, 11.38, 11.47,
11.49
Root test for infinite series, 37.91
to 37.94, 37.105, 37.106,
38.20, 38.23
Roots:
cube (see Cube roots)
of polynomials, 5.76 to 5.82, 11.28
square (see Square roots)
Roses (curves), 35.33, 35.47, 35.48,
35.58, 35.64, 35.65, 35.72,
35.93
Ruled surfaces, 41.29, 41.30
Saddle surface, 41.19, 41.84
Scalar projection of vectors, 33.4,
40.33
Second derivative test for relative
extrema, 13.1, 13.3 to 13.7,
13.20, 13.21, 15.1 to 15.9,
15.12, 15.13, 15.16to 15.18,
15.20to 15.29, 15.32, 15.33,
15.35, 15.37, 15.39 to 15.56
(See also First derivative test for
relative extrema)
Segments of disks, 29.43
Self-inverse functions, 5.69, 5.74,
5.75
Sequences:
infinite (see Infinite sequences)
sum of cubes of integers, 20.65
sum of integers, 20.4
Series (see Infinite series)
Simpson's rule for approximating
integrals, 20.68, 20.69, 23.73
Sketches (see Graphs)
Slope:
of curves, 34.28
of lines, 3.1,3.5, 3.46,3.61 to
3.65
in polar coordinates, 35.93,
35.94, 35.96, 35.97
Slope-intercept equations of lines,
3.6 to 3.11, 3.20, 3.21,3.27,
3.29 to 3.31, 3.34, 3.35,
3.41, 3.44, 3.46, 3.52 to
3.60, 8.13, 8.16, 8.36, 9.13,
9.14
Spheres:
cones circumscribed about, 16.42
equations of, 40.6 to 40.12,
40.16,40.22,40.23,41.76,
41.86
graphs of, 41.31
as level surfaces, 41.47
planes tangent to, 40.94
surface area of, 14.13, 14.37,
14.43, 31.2, 44.57
surface area of caps of, 31.15
volume of, 14.7, 14.13, 14.35,
14.37, 14.43, 14.48, 22.1,
44.34, 44.50
Spherical coordinates, 41.85 to
41.98
Spherical segment volume, 14.41
Spirals:
Archimedean, 35.70, 35.76,
35.103, 35.110
degenerate, 35.111
Spirals (Cont.):
equiangular, 35.71, 35.77, 35.101,
35.112
logarithmic, 34.42
Square roots:
approximation of, 18.2, 18.3,
18.20, 18.33
in limits, 6.9, 6.23 to 6.27, 6.29
to 6.31, 6.38, 6.40,6.41,
6.52
Squares, completing, 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
Strictly increasing functions,
11.48
Strictly positive functions, 11.48
Sum rule:
for derivatives, 8.7, 9.11
for limits, 36.49
Sums:
of cubes of integers, 20.65
of integers, 20.4
partial, 37.4, 37.5, 37.10, 37.17
to 37.22, 37.24, 37.25
Supply and demand equations,
3.82, 16.32, 16.33
Surface area:
cone, 16.9,31.14,44.58
cylinder, 16.22, 42.89
by integration, 31.1 to 31.15,
32.41, 35.84 to 35.86, 44.53
to 44.58
sphere, 14.13, 14.37, 14.43, 31.2,
44.57
spherical cap, 31.15
Surface normal vectors,
42.31
Surfaces:
level, 41.44 to 41.47
of revolution, 41.4 to 41.12
ruled, 41.29, 41.30
saddle, 41.19, 41.84
Tangent lines, 4.15, 4.19 to 4.22,
8.13 to 8.15, 8.18, 8.20,
8.23, 8.28, 8.34, 8.35, 8.38,
8.42,9.13,9.19,9.23, 10.22,
10.23, 10.25, 10.28, 10.32 to
10.35, 10.47, 11.44, 12.14,
12.16, 12.18, 12.27, 12.28,
12.37, 12.42 to 12.46, 15.21,
15.28, 15.29, 19.66 to 19.70,
19.77, 19.83to 19.86,21.46,
24.56, 27.58, 34.26, 34.31,
35.89 to 35.92, 35.95, 35.98,
42.26 to 42.33, 42.119, 45.1,
45.4, 45.6
Tangent planes, 42.31, 42.105 to
42.115, 42.122 to 42.126
Rectangular coordinates:
cylindrical coordinates and,
41.67, 41.70 to 41.74, 41.80
to 41.85
cylindrical-to-rectangular
transformations, 41.67
polar-to-rectangular
transformations, 35.1, 35.4
to 35.6, 41.67
rectangular-to-cylindrical
transformations, 41.67
rectangular-to-polar
transformations, 35.1 to
35.3, 35.21 to 35.27, 41.67
rectangular-to-spherical
transformations, 41.85
spherical coordinates and, 41.85,
41.88 to 41.93
spherical-to-rectangular
transformations, 41.85
Rectangular form of vectors, 33.14
to 33.16
Rectilinear motion, 17.1 to 17.35,
19.34 to 19.39, 19.41, 19.44,
19.57, 19.59, 19.72 to 19.76
Reflections of curves and lines,
5.94 to 5.100
Related rates, 14.1 to 14.56
Relative extrema (see Extrema of
functions, relative)
Removable discontinuities, 7.5, 7.9
Repeating decimals as infinite
series, 37.8, 37.9, 37.26
Revolution:
surface of, 41.4 to 41.12
volume of, 31.33 to 31.35
Rhombuses:
diagonals of, 33.32
as parallelograms, 3.76
Riccati equation, 46.43, 46.44
Right angles, 33.12
Right-hand limits, 6.5, 6.33 to 6.36,
6.39
Right triangles:
area of, 40.36
centroidof, 31.28, 31.34
perimeter of, 16.19
Pythagorean theorem for, 4.21,
14.1, 14.5,40.34
vertices of, 3.25, 3.26, 40.13
Rolle's theorem, 11.1 to 11.9,
11.27, 11.31, 11.38, 11.47,
11.49
Root test for infinite series, 37.91
to 37.94, 37.105, 37.106,
38.20, 38.23
Roots:
cube (see Cube roots)
of polynomials, 5.76 to 5.82, 11.28
square (see Square roots)
Roses (curves), 35.33, 35.47, 35.48,
35.58, 35.64, 35.65, 35.72,
35.93
Ruled surfaces, 41.29, 41.30
Saddle surface, 41.19, 41.84
Scalar projection of vectors, 33.4,
40.33
Second derivative test for relative
extrema, 13.1, 13.3 to 13.7,
13.20, 13.21, 15.1 to 15.9,
15.12, 15.13, 15.16to 15.18,
15.20to 15.29, 15.32, 15.33,
15.35, 15.37, 15.39 to 15.56
(See also First derivative test for
relative extrema)
Segments of disks, 29.43
Self-inverse functions, 5.69, 5.74,
5.75
Sequences:
infinite (see Infinite sequences)
sum of cubes of integers, 20.65
sum of integers, 20.4
Series (see Infinite series)
Simpson's rule for approximating
integrals, 20.68, 20.69, 23.73
Sketches (see Graphs)
Slope:
of curves, 34.28
of lines, 3.1,3.5, 3.46,3.61 to
3.65
in polar coordinates, 35.93,
35.94, 35.96, 35.97
Slope-intercept equations of lines,
3.6 to 3.11, 3.20, 3.21,3.27,
3.29 to 3.31, 3.34, 3.35,
3.41, 3.44, 3.46, 3.52 to
3.60, 8.13, 8.16, 8.36, 9.13,
9.14
Spheres:
cones circumscribed about, 16.42
equations of, 40.6 to 40.12,
40.16,40.22,40.23,41.76,
41.86
graphs of, 41.31
as level surfaces, 41.47
planes tangent to, 40.94
surface area of, 14.13, 14.37,
14.43, 31.2, 44.57
surface area of caps of, 31.15
volume of, 14.7, 14.13, 14.35,
14.37, 14.43, 14.48, 22.1,
44.34, 44.50
Spherical coordinates, 41.85 to
41.98
Spherical segment volume, 14.41
Spirals:
Archimedean, 35.70, 35.76,
35.103, 35.110
degenerate, 35.111
Spirals (Cont.):
equiangular, 35.71, 35.77, 35.101,
35.112
logarithmic, 34.42
Square roots:
approximation of, 18.2, 18.3,
18.20, 18.33
in limits, 6.9, 6.23 to 6.27, 6.29
to 6.31, 6.38, 6.40,6.41,
6.52
Squares, completing, 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
Strictly increasing functions,
11.48
Strictly positive functions, 11.48
Sum rule:
for derivatives, 8.7, 9.11
for limits, 36.49
Sums:
of cubes of integers, 20.65
of integers, 20.4
partial, 37.4, 37.5, 37.10, 37.17
to 37.22, 37.24, 37.25
Supply and demand equations,
3.82, 16.32, 16.33
Surface area:
cone, 16.9,31.14,44.58
cylinder, 16.22, 42.89
by integration, 31.1 to 31.15,
32.41, 35.84 to 35.86, 44.53
to 44.58
sphere, 14.13, 14.37, 14.43, 31.2,
44.57
spherical cap, 31.15
Surface normal vectors,
42.31
Surfaces:
level, 41.44 to 41.47
of revolution, 41.4 to 41.12
ruled, 41.29, 41.30
saddle, 41.19, 41.84
Tangent lines, 4.15, 4.19 to 4.22,
8.13 to 8.15, 8.18, 8.20,
8.23, 8.28, 8.34, 8.35, 8.38,
8.42,9.13,9.19,9.23, 10.22,
10.23, 10.25, 10.28, 10.32 to
10.35, 10.47, 11.44, 12.14,
12.16, 12.18, 12.27, 12.28,
12.37, 12.42 to 12.46, 15.21,
15.28, 15.29, 19.66 to 19.70,
19.77, 19.83to 19.86,21.46,
24.56, 27.58, 34.26, 34.31,
35.89 to 35.92, 35.95, 35.98,
42.26 to 42.33, 42.119, 45.1,
45.4, 45.6
Tangent planes, 42.31, 42.105 to
42.115, 42.122 to 42.126