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Active Calculus

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
sequence, Definition
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
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
sequence, Definition
Divergence Test, Paragraph
domain, Paragraph
dominates, Exercise
equilibrium solution, Paragraph
stable, Item
unstable, Item
error, Item
error function, Example Paragraph
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
geometric series, Paragraph
common ratio, Paragraph
harmonic series, Paragraph
Hooke’s Law, Item
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
instantaneous rate of change, Paragraph Paragraph
instantaneous velocity, Paragraph Paragraph
integral function, Paragraph
integral sign, Paragraph
integral test, Subsection Paragraph
integrand, Paragraph
integration by parts, Subsection
interval of convergence, Subsection
Lagrange error bound, Assemblage
left limit, Paragraph
lemniscate, Paragraph
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
L’Hôpital’s rule, Assemblage
L’Hôpital’s rule (at infinity), Assemblage
Maclaurin series, Paragraph
mass, Paragraph
absolute, Definition
global, Definition
local, Definition
relative, Definition
midpoint rule
error, Item
absolute, Definition
global, Definition
local, Definition
relative, Definition
net signed area, Paragraph
Newton-meter, Paragraph
Newton’s Law of Cooling, Exercise
one-to-one, Item
onto, Item
partial fractions, Subsection
partial sum, Paragraph Paragraph
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
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
washer method, Paragraph
weighted average, Paragraph Paragraph