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IndexIndex

aa@\("!\), Definition
Absolute Convergence Theorem, Theorem
absolute maximum, Definition
absolute minimum, Definition
Absolute Value Theorem, Theorem
acceleration, Paragraph, Item
Alternating Harmonic Series, Item, Paragraph, Paragraph
Alternating Series Test
for series, Theorem
an@\(a_\text{N}\), Paragraph, Paragraph
analytic function, Paragraph
angle of elevation, Paragraph
antiderivative, Definition
arc length, Key Idea, Theorem, Paragraph, Theorem, Paragraph
arc length parameter, Paragraph, Theorem
asymptote
horizontal, Item
vertical, Paragraph
at@\(a_\text{T}\), Paragraph, Paragraph
average rate of change, Definition
average value of a function, Definition
average value of function, Definition
average velocity, Paragraph
Binomial Series, Paragraph
Bisection Method, Paragraph
boundary point, Definition
bounded sequence, Definition
convergence, Theorem
bounded set, Definition
center of mass, Paragraph, Theorem, Theorem, Theorem, Definition
Chain Rule, Theorem
multivariable, Theorem, Item
notation, Paragraph
circle of curvature, Paragraph
closed, Definition
closed disk, Definition
concave down, Definition
concave up, Definition
concavity, Definition, Paragraph
inflection point, Theorem
test for, Theorem
conic sections, Paragraph
degenerate, Paragraph
ellipse, Definition
hyperbola, Definition
parabola, Definition
Constant Multiple Rule
of derivatives, Item
of integration, Item
of series, Item
constrained optimization, Paragraph
continuous
at \(c\), Item
everywhere, Item
on \(I\), Item
continuous function, Definition, Item
properties, Theorem, Theorem
vector–valued, Definition, Theorem
contour lines, Paragraph
convergence
absolute, Item, Theorem
Alternating Series Test, Theorem
conditional, Item
Direct Comparison Test, Theorem
Direct Comparison Test!for integration, Item
Integral Test, Theorem
interval of, Item
Limit Comparison Test, Theorem
Limit Comparison Test!for integration, Theorem
nth@\(n^\text{ th }\)–term test, Theorem
of geometric series, Item
of improper int., Item, Item, Item, Theorem
of monotonic sequences, Item
of p@of \(p\)-series, Theorem
of power series, Theorem
of sequence, Definition, Theorem
of series, Item
radius of, Item
Ratio Comparison Test, Theorem
Root Comparison Test, Theorem
critical number, Definition
critical point, Definition, Definition, Theorem, Definition
cross product
and derivatives, Theorem
applications, Paragraph
applications!area of parallelogram, Paragraph
applications!torque, Paragraph
applications!volume of parallelepiped, Paragraph
definition, Definition
properties, Theorem, Theorem
curvature, Definition
and motion, Paragraph
equations for, Theorem
of circle, Example, Paragraph
radius of, Paragraph
curve
parametrically defined, Definition
rectangular equation, Paragraph
smooth, Definition
curve sketching, Key Idea
cusp, Definition
cycloid, Example
cylinder, Definition
decreasing function, Definition
finding intervals, Key Idea
strictly, Definition
definite integral, Definition
and substitution, Theorem
properties, Theorem
derivative
acceleration, Key Idea
as a function, Definition
at a point, Definition
basic rules, Theorem
Chain Rule, Theorem, Paragraph, Theorem, Item
Constant Multiple Rule, Item
Constant Rule, Item
differential, Definition
directional, Definition, Theorem, Key Idea, Item, Definition, Theorem
exponential functions, Theorem
First Deriv. Test, Theorem
Generalized Power Rule, Theorem
higher order, Definition
higher order!interpretation, Paragraph
hyperbolic funct., Item
implicit, Paragraph, Theorem
interpretation, Paragraph
inverse function, Paragraph
inverse hyper., Item
inverse trig., Theorem
Mean Value Theorem, Theorem
mixed partial, Definition
motion, Key Idea
multivariable differentiability, Item, Definition
normal line, Definition
notation, Definition, Definition
parametric equations, Key Idea
partial, Definition, Definition
Power Rule, Item, Theorem, Theorem
power series, Item
Product Rule, Theorem
Quotient Rule, Theorem
Second Deriv. Test, Theorem
Sum/Difference Rule, Item
tangent line, Definition
trigonometric functions, Item
vector–valued functions, Definition, Item, Theorem
velocity, Key Idea
difference quotient, Paragraph
differentiable, Definition, Item, Definition
differential, Definition
notation, Key Idea
Direct Comparison Test
for integration, Item
for series, Theorem
directional derivative, Definition, Theorem, Key Idea, Item, Definition, Theorem
directrix, Definition, Definition
Disk Method, Key Idea
displacement, Paragraph, Paragraph, Paragraph
distance
between lines, Item
between point and line, Item
between point and plane, Key Idea
between points in space, Definition
traveled, Theorem
divergence
Alternating Series Test, Theorem
Direct Comparison Test, Theorem
Direct Comparison Test!for integration, Item
Integral Test, Theorem
Limit Comparison Test, Theorem
Limit Comparison Test!for integration, Theorem
nth@\(n^\text{ th }\)–term test, Theorem
of geometric series, Item
of improper int., Item, Item, Item, Theorem
of p@of \(p\)-series, Theorem
of sequence, Definition
of series, Item
Ratio Comparison Test, Theorem
Root Comparison Test, Theorem
dot product
and derivatives, Theorem
definition, Item
properties, Theorem, Theorem
double integral, Definition, Theorem
in polar, Key Idea
properties, Theorem
eccentricity, Definition, Definition
elementary function, Paragraph
ellipse
definition, Definition
eccentricity, Definition
parametric equations, Item
reflective property, Theorem
standard equation, Key Idea
extrema
absolute, Definition, Definition
and First Deriv. Test, Theorem
and Second Deriv. Test, Theorem
finding, Key Idea
relative, Item, Definition, Theorem
Extreme Value Theorem, Theorem, Theorem
extreme values, Definition
factorial, Definition
First Derivative Test, Theorem
floor function, Example
fluid pressure/force, Definition, Key Idea
focus, Definition, Definition, Definition
Fubini's Theorem, Theorem
function
of three variables, Definition
of two variables, Definition
vector-valued, Definition
Fundamental Theorem of Calculus, Theorem, Theorem
and Chain Rule, Paragraph
Gabriel's Horn, Example
Generalized Power Rule, Theorem
geometric series, Definition, Item
gradient, Definition, Key Idea, Item, Definition, Theorem, Definition
and level curves, Item
and level surfaces, Theorem
Harmonic Series, Item
Head To Tail Rule, Paragraph
Hooke's Law, Paragraph
hyperbola
definition, Definition
eccentricity, Definition
parametric equations, Item
reflective property, Theorem
standard equation, Key Idea
hyperbolic function
definition, Item
derivatives, Item
identities, Item
integrals, Item
inverse, Paragraph
inverse!derivative, Item
inverse!integration, Item
inverse!logarithmic def., Item
implicit differentiation, Paragraph, Theorem
improper integration, Item, Definition
increasing function, Definition
finding intervals, Key Idea
strictly, Definition
indefinite integral, Definition
indeterminate form, Paragraph, Paragraph, Paragraph, Key Idea
inflection point, Definition
initial point, Definition
initial value problem, Paragraph
Integral Test, Theorem
integration
arc length, Key Idea
area, Definition, Paragraph, Item
area between curves, Paragraph, Theorem
average value, Definition
by parts, Theorem
by substitution, Theorem
definite, Definition
definite!and substitution, Theorem
definite!properties, Theorem
definite!Riemann Sums, Theorem
displacement, Paragraph
distance traveled, Theorem
double, Definition
fluid force, Definition, Key Idea
Fun. Thm. of Calc., Theorem, Theorem
general application technique, Key Idea
hyperbolic funct., Item
improper, Item, Definition, Item, Theorem
indefinite, Definition
inverse hyper., Item
iterated, Definition
Mean Value Theorem, Theorem
multiple, Definition
notation, Paragraph, Definition, Paragraph, Definition
numerical, Paragraph
numerical!Left/Right Hand Rule, Paragraph, Key Idea
numerical!Simpson's Rule, Paragraph, Key Idea, [ol]
numerical!Trapezoidal Rule, Paragraph, Key Idea, [ol]
of multivariable functions, Paragraph
of power series, Item
of trig. functions, Theorem
of trig. powers, Key Idea, Key Idea
of vector–valued functions, Theorem
partial fraction decomp., Key Idea
Power Rule, Item
Sum/Difference Rule, Item
surface area, Key Idea, Key Idea, Key Idea
trig. subst., Item
triple, Definition, Theorem, Definition, Definition, Theorem
volume!cross-sectional area, Theorem
volume!Disk Method, Key Idea
volume!Shell Method, Key Idea, Key Idea
volume!Washer Method, Key Idea, Key Idea
work, Key Idea
interior point, Definition
Intermediate Value Theorem, Theorem
interval of convergence, Item
iterated integration, Definition, Definition, Theorem, Definition, Theorem, Definition, Definition, Theorem
changing order, Paragraph
properties, Theorem, Theorem
L'Hôpital's Rule, Theorem, Item
lamina, Paragraph
Left Hand Rule, Paragraph, Paragraph, Paragraph
Left/Right Hand Rule, Key Idea
level curves, Paragraph, Item
level surface, Paragraph, Theorem
limit
Absolute Value Theorem, Theorem
at infinity, Item
definition, Definition
difference quotient, Paragraph
does not exist, Paragraph, Theorem
indeterminate form, Paragraph, Paragraph, Paragraph, Paragraph, Key Idea
L'Hôpital's Rule, Theorem, Item
left-handed, Item
of infinity, Definition
of multivariable function, Definition, Theorem, Item
of sequence, Definition
of vector–valued functions, Definition, Item
one sided, Item, Item
properties, Theorem, Theorem
pseudo-definition, Paragraph
right-handed, Item
Squeeze Theorem, Theorem
Limit Comparison Test
for integration, Theorem
for series, Theorem
lines, Paragraph
distances between, Item
equations for, Definition
intersecting, Paragraph
parallel, Paragraph
skew, Paragraph
logarithmic differentiation, Paragraph
Maclaurin Polynomial
definition, Definition
Maclaurin Polynomial|see{Taylor Polynomial}, Definition
Maclaurin Series
definition, Definition
Maclaurin Series|see{Taylor Series}, Definition
magnitude of vector, Definition
mass, Paragraph, Definition, Definition
center of, Paragraph
maximum
absolute, Definition, Definition
and First Deriv. Test, Theorem
and Second Deriv. Test, Theorem
relative/local, Item, Definition, Theorem
Mean Value Theorem
of differentiation, Theorem
of integration, Theorem
Midpoint Rule, Paragraph, Paragraph
minimum
absolute, Definition, Definition
and First Deriv. Test, Theorem, Theorem
relative/local, Item, Definition, Theorem
moment, Definition, Theorem, Definition
monotonic sequence, Item
multiple integration|see{iterated integration}, Definition
multivariable function, Definition, Definition
continuity, Item, Theorem, Item, Theorem, Item
differentiability, Item, Theorem, Theorem, Definition, Item
domain, Definition, Definition
level curves, Paragraph
level surface, Paragraph
limit, Definition, Theorem, Item
range, Definition, Definition
Newton's Method, Key Idea
norm, Definition
normal line, Definition, Definition, Definition
normal vector, Paragraph
nth@\(n^\text{ th }\)–term test, Theorem
numerical integration, Paragraph
Left/Right Hand Rule, Paragraph, Key Idea
Simpson's Rule, Paragraph, Key Idea
Simpson's Rule!error bounds, [ol]
Trapezoidal Rule, Paragraph, Key Idea
Trapezoidal Rule!error bounds, [ol]
open, Definition
open ball, Item
open disk, Definition
optimization, Paragraph
constrained, Paragraph
orthogonal, Definition, Definition
decomposition, Key Idea
orthogonal decomposition of vectors, Key Idea
orthogonal projection, Definition
osculating circle, Paragraph
p@\(p\)-series, Item, Theorem
parabola
definition, Definition
general equation, Key Idea
reflective property, Item
parallel vectors, Item
Parallelogram Law, Paragraph
parametric equations
arc length, Theorem
concavity, Paragraph
definition, Definition
finding \(\frac{d^2y}{dx^2}\), Key Idea
finding \(\frac{dy}{dx}\), Key Idea
normal line, Definition
surface area, Key Idea
tangent line, Definition
partial derivative, Definition, Definition
high order, Paragraph
meaning, Paragraph
mixed, Definition
second derivative, Definition
total differential, Definition, Definition
perpendicular|see{orthogonal}, Definition
planes
coordinate plane, Paragraph
distance between point and plane, Key Idea
equations of, Definition
introduction, Paragraph
normal vector, Paragraph
tangent, Definition
point of inflection, Definition
polar
coordinates, Paragraph
function!arc length, Paragraph
function!gallery of graphs, Paragraph
function!surface area, Key Idea
functions, Paragraph
functions!area, Paragraph
functions!area between curves, Paragraph
functions!finding \(\frac{dy}{dx}\), Key Idea
functions!graphing, Paragraph
polar coordinates, Paragraph
plotting points, Example
Power Rule
differentiation, Item, Theorem, Theorem, Theorem
integration, Item
power series, Definition
algebra of, Theorem
convergence, Theorem
derivatives and integrals, Item
projectile motion, Paragraph, Key Idea, Example
quadric surface
definition, Definition
ellipsoid, Figure
elliptic cone, Figure
elliptic paraboloid, Figure
gallery|(, Figure
gallery|), Figure
hyperbolic paraboloid, Figure
hyperboloid of one sheet, Figure
hyperboloid of two sheets, Figure
sphere, Figure
trace, Paragraph
Quotient Rule, Theorem
r@\(\mathbb{R}\), Paragraph
radius of convergence, Item
radius of curvature, Paragraph
Ratio Comparison Test
for series, Theorem
rearrangements of series, Paragraph, Theorem
related rates, Paragraph, Key Idea
Riemann Sum, Paragraph, Definition
and definite integral, Theorem
Right Hand Rule, Paragraph, Paragraph, Paragraph
of Cartesian coordinates, Paragraph
Rolle's Theorem, Theorem
Root Comparison Test
for series, Theorem
saddle point, Definition, Theorem
Second Derivative Test, Theorem, Theorem
sensitivity analysis, Paragraph
sequence
Absolute Value Theorem, Theorem
positive, Subsection
sequences
boundedness, Definition
convergent, Definition, Theorem, Item
definition, Definition
divergent, Definition
limit, Definition
limit properties, Item
monotonic, Item
series
absolute convergence, Item
Absolute Convergence Theorem, Theorem
alternating, Definition
Alternating Series Test, Theorem
alternating!Approximation Theorem, Theorem
Binomial, Paragraph
conditional convergence, Item
convergent, Item
definition, Item
Direct Comparison Test, Theorem
divergent, Item
geometric, Definition, Item
Integral Test, Theorem
interval of convergence, Item
Limit Comparison Test, Theorem
Maclaurin, Definition
nth@\(n^\text{ th }\)–term test, Theorem
p@\(p\)-series, Item, Theorem
partial sums, Item
power, Definition, Theorem
power!derivatives and integrals, Item
properties, Item
radius of convergence, Item
Ratio Comparison Test, Theorem
rearrangements, Paragraph, Theorem
Root Comparison Test, Theorem
Taylor, Definition
telescoping, Example, Paragraph
Shell Method, Key Idea, Key Idea
signed area, Definition
signed volume, Definition, Theorem
Simpson's Rule, Paragraph, Key Idea
error bounds, [ol]
smooth, Definition
smooth curve, Definition
speed, Item
sphere, Paragraph
Squeeze Theorem, Theorem
Sum/Difference Rule
of derivatives, Item
of integration, Item
of series, Item
summation
notation, Paragraph
surface area, Definition
solid of revolution, Key Idea, Key Idea, Key Idea
surface of revolution, Key Idea, Key Idea
tangent line, Definition, Definition, Key Idea, Definition
directional, Definition
tangent plane, Definition
Taylor Polynomial
definition, Definition
Taylor's Theorem, Item
Taylor Series
common series, Key Idea
definition, Definition
equality with generating function, Theorem
Taylor's Theorem, Item
telescoping series, Example, Paragraph
terminal point, Definition
total differential, Definition, Definition
sensitivity analysis, Paragraph
total signed area, Definition
trace, Paragraph
Trapezoidal Rule, Paragraph, Key Idea
error bounds, [ol]
triple integral, Definition, Theorem, Definition, Definition, Theorem
properties, Theorem
unbounded sequence, Definition
unbounded set, Definition
unit normal vector
an@\(a_\text{N}\), Paragraph
and acceleration, Paragraph, Paragraph
and curvature, Paragraph
definition, Definition
in \(\mathbb{R}^2\), Theorem
unit tangent vector
and acceleration, Paragraph, Paragraph
and curvature, Definition, Paragraph
at@\(a_\text{T}\), Paragraph
definition, Definition
in \(\mathbb{R}^2\), Theorem
unit vector, Definition
properties, Item
standard unit vector, Item
unit normal vector, Definition
unit tangent vector, Definition
vector-valued function
algebra of, Definition
average rate of change, Definition
definition, Definition
displacement, Paragraph
graphing, Paragraph
of constant length, Paragraph
vectors, Definition
algebra of, Item
algebraic properties, Theorem
component form, Definition
cross product, Definition, Theorem, Theorem
definition, Definition
dot product, Item, Theorem, Theorem
Head To Tail Rule, Paragraph
magnitude, Definition
norm, Definition
normal vector, Paragraph
orthogonal, Definition
orthogonal decomposition, Key Idea
orthogonal projection, Definition
parallel, Item
Parallelogram Law, Paragraph
resultant, Paragraph
standard unit vector, Item
unit vector, Definition, Item
zero vector, Paragraph
vector–valued function
arc length, Theorem
continuity, Definition, Theorem
derivatives, Definition, Item, Theorem
describing motion, Item
distance traveled, Theorem
integration, Theorem
limits, Definition, Item
of constant length, Theorem, Paragraph, Key Idea
projectile motion, Paragraph, Key Idea
smooth, Definition
tangent line, Definition
velocity, Paragraph, Item
average velocity, Paragraph
volume, Definition, Theorem, Theorem
Washer Method, Key Idea, Key Idea
work, Key Idea, Definition