# IndexIndex

aa@\("!\), Definition

Absolute Convergence Theorem, Theorem

absolute maximum, Definition

absolute minimum, Definition

Absolute Value Theorem, Theorem

Alternating Series Test

for series, Theorem

analytic function, Paragraph

angle of elevation, Paragraph

antiderivative, Definition

asymptote

horizontal, Item

vertical, 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

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

vector–valued, Definition, Theorem

contour lines, Paragraph

convergence

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 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

curvature, Definition

and motion, Paragraph

equations for, Theorem

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

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

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 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

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 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

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 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

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

improper integration, Item, Definition

increasing function, Definition

finding intervals, Key Idea

strictly, Definition

indefinite integral, Definition

inflection point, Definition

initial point, Definition

initial value problem, Paragraph

Integral Test, Theorem

integration

arc length, Key Idea

area, Definition, Paragraph, Item

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

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

of multivariable functions, Paragraph

of power series, Item

of trig. functions, Theorem

of vector–valued functions, Theorem

partial fraction decomp., Key Idea

Power Rule, Item

Sum/Difference Rule, Item

trig. subst., Item

triple, Definition, Theorem, Definition, Definition, Theorem

volume!cross-sectional area, Theorem

volume!Disk Method, 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

lamina, Paragraph

Left/Right Hand Rule, Key Idea

limit

Absolute Value Theorem, Theorem

at infinity, Item

definition, Definition

difference quotient, Paragraph

left-handed, Item

of infinity, Definition

of multivariable function, Definition, Theorem, Item

of sequence, Definition

of vector–valued functions, Definition, Item

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

minimum

absolute, Definition, Definition

relative/local, Item, Definition, Theorem

moment, Definition, Theorem, Definition

monotonic sequence, Item

multiple integration|see{iterated integration}, Definition

multivariable function, Definition, Definition

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

Simpson's Rule!error bounds, [ol]

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

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

integration, Item

power series, Definition

algebra of, Theorem

convergence, Theorem

derivatives and integrals, Item

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

Riemann Sum, Paragraph, Definition

and definite integral, Theorem

of Cartesian coordinates, Paragraph

Rolle's Theorem, Theorem

Root Comparison Test

for series, Theorem

saddle point, Definition, 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

partial sums, Item

power, Definition, Theorem

power!derivatives and integrals, Item

properties, Item

radius of convergence, Item

Ratio Comparison Test, Theorem

Root Comparison Test, Theorem

Taylor, Definition

signed area, Definition

signed volume, Definition, Theorem

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

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

terminal point, Definition

total differential, Definition, Definition

sensitivity analysis, Paragraph

total signed area, Definition

trace, Paragraph

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 curvature, Paragraph

definition, Definition

in \(\mathbb{R}^2\), Theorem

unit tangent vector

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

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

smooth, Definition

tangent line, Definition

average velocity, Paragraph

volume, Definition, Theorem, Theorem

work, Key Idea, Definition