177
Index
dA, 104
ds, 87, 92
p-series test, 130
Absolute convergence test, 134
Alternating series test, 135
Arc length
differential of, 85
formula for, 87
Center of mass, 108, 110
Choosing a convergence test, 140
Classifying critical points
in three dimensions, 37
Classifying multivariate critical points, 37
Combinations of sequences, 119
Comparison test, 131
Constrained optimization, 57
Convergence
choosing a test, 140
of a sequence, 115
of a series, 122, 126
of bounded monotone sequences, 118
of the tail of a sequence, 138
Critical points
in three dimensions, 34, 36
Curves
level, 19
Decomposable integral, 100
Derivative
partial, 2, 3
order of, 6
Differential
of area, 104
Differential of arc length, 85
formula for, 87
Direction of a level curve, 20
Directional derivative
of a function, 18
Discriminant
of a system, 37
Distance
definition of, 41
optimizing, 43
Divergence test, 128
Factorial, 136
General term
of a series, 127
Geometric series, 123
Gradient
of a function, 10
Harmonic series, 127
Higher-order partial derivatives, 6
Implicit partial derivatives, 5
Integral
decomposable, 100
iterated, 98
multiple, 97, 98
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