## Index Index

\(u\)-substitution, Subsection

absolute convergence, Subsection

acceleration, Item

alternating series, Paragraph

alternating series estimation theorem, Paragraph

alternating series test, Paragraph

antiderivative, Definition

graph, Subsection

antidifferentiation, Subsection

arc length, Subsection Assemblage

arcsine, Subsection

area, Subsection

under velocity function, Subsection

asymptote, Paragraph

horizontal, Paragraph

vertical, Paragraph

autonomous, Paragraph

average rate of change, Definition

average value, Assemblage

average value of a function, Subsection

average velocity, Assemblage Item

backward difference, Paragraph

carrying capacity, Paragraph

center of mass (continuous mass distribution), Assemblage

center of mass (point-masses, Assemblage

central difference, Paragraph

chain rule, Assemblage

codomain, Paragraph

composition, Paragraph

concave down, Definition

concave up, Definition

concavity, Paragraph

conditional convergence, Subsection

constant multiple rule, Assemblage

continuous, Subsection

continuous at \(x = a\), Definition

converge

sequence, Definition

convergence

absolute, Subsection

conditional, Subsection

convergent sequence, Definition

cosecant, Subsection

cotangent, Subsection

critical number, Definition

critical point, Paragraph

critical value, Paragraph

cusp, Item

decreasing, Paragraph

definite integral

constant multiple rule, Assemblage

definition, Subsection Definition

sum rule, Assemblage

density, Subsection

derivative

arcsine, Assemblage

constant function, Assemblage

cosine, Assemblage

cotangent, Assemblage

definition, Definition Paragraph

exponential function, Assemblage

inverse, Assemblage

logarithm, Assemblage

power function, Assemblage

sine, Assemblage

tangent, Assemblage

difference quotient, Paragraph

differentiable, Item Subsection

differential equation, Subsection

autonomous, Paragraph

first order, Paragraph

solution, Subsection

disk method, Paragraph

distance traveled, Subsection

diverge

sequence, Definition

Divergence Test, Paragraph

domain, Paragraph

dominates, Exercise

equilibrium solution, Paragraph

stable, Item

unstable, Item

error, Item

Euler's Method, Subsection

error, Subsection

extreme value, Paragraph

extreme value theorem, Assemblage

Fibonacci sequence, Section

finite geometric series, Paragraph

first derivative test, Paragraph Assemblage

foot-pound, Paragraph

forward difference, Paragraph

FTC, Paragraph

function, Paragraph

function-derivative pair, Paragraph

Fundamental Theorem of Calculus

First, Paragraph

Second, Subsection

fundamental theorem of calculus, Subsection Assemblage

implicit function, Paragraph

improper integral, Subsection

converges, Assemblage

diverges, Assemblage

unbounded integrand, Paragraph

unbounded region of integration, Paragraph

increasing, Paragraph

indefinite integral, Paragraph

evaluate, Paragraph

indeterminate form, Example

infinite series, Paragraph

infinity, Paragraph

inflection point, Definition

initial condition, Paragraph

integral function, Paragraph

integral sign, Paragraph

integral test, Subsection Paragraph

integrand, Paragraph

integration by parts, Subsection

interval of convergence, Subsection

L'Hôpital's rule, Assemblage

L'Hôpital's rule (at infinity), Assemblage

Lagrange error bound, Assemblage

left limit, Paragraph

lemniscate, Paragraph

limit

definition, Definition

one-sided, Paragraph

limit comparison test, Subsection

limits of integration, Paragraph

local linearization, Subsection

locally linear, Paragraph

logistic, Subsection

logistic equation, Paragraph

solution, Assemblage

Maclaurin series, Paragraph

mass, Paragraph

maximum

absolute, Definition

global, Definition

local, Definition

relative, Definition

midpoint rule

error, Item

minimum

absolute, Definition

global, Definition

local, Definition

relative, Definition

partial fractions, Subsection

per capita growth rate, Paragraph

position, Paragraph

power series, Subsection

definition, Definition

power series differentiation and integration theorem, Assemblage

product rule, Paragraph Assemblage

quotient rule, Assemblage

ratio test, Subsection

related rates, Paragraph

Riemann sum, Paragraph

left, Paragraph

middle, Paragraph

right, Paragraph

right limit, Paragraph

secant, Subsection

secant line, Paragraph

second derivative, Subsection Paragraph

second derivative test, Assemblage

second fundamental theorem of calculus, Assemblage

separable, Paragraph Subsection

sequence, Subsection

term, Paragraph

sequence of partial sums, Paragraph

series

converges, Paragraph

diverges, Paragraph

geometric, Paragraph

sigma notation, Paragraph

Simpson's rule, Subsection

slope field, Subsection Paragraph

solid of revolution, Subsection

stable, Item

sum rule, Assemblage

tangent, Item

tangent line, Paragraph

equation, Subsection

Taylor polynomial, Paragraph

error, Subsection

Taylor polynomials, Subsection

Taylor series, Subsection Definition

interval of convergence, Subsection

radius of convergence, Paragraph

total change theorem, Subsection Assemblage

trapezoid rule, Subsection

error, Item

triangular numbers, Section

trigonometry, Paragraph

fundamental trigonometric identity, Paragraph

unstable, Item