# Active Calculus

## IndexIndex

$$u$$-substitution
acceleration, Item
antiderivative
general
graph
antidifferentiation
arc length
arcsine
area
under velocity function
asymptote
horizontal
vertical
autonomous
average rate of change
average value
average value of a function
average velocity
backward difference
carrying capacity
center of mass (continuous mass distribution)
center of mass (point-masses
central difference
chain rule
codomain
composition
concave down
concave up
concavity
constant multiple rule
continuous
continuous at $$x = a$$
cosecant
cotangent
critical number
critical point
critical value
cusp, Item
decreasing
definite integral
constant multiple rule
definition
sum rule
density
derivative
arcsine
constant function
cosine
cotangent
definition
exponential function
inverse
logarithm
power function
sine
tangent
difference quotient
differentiable
differential equation
autonomous
first order
solution
disk method
distance traveled
domain
dominates
equilibrium solution
stable, Item
unstable, Item
error, Item
error function
Euler’s Method
error
extreme value
extreme value theorem
first derivative test
folium of Descartes
foot-pound
forward difference
FTC
function
function-derivative pair
Fundamental Theorem of Calculus
First
Second
fundamental theorem of calculus
Hooke’s Law, Item
implicit function
improper integral
converges
diverges
unbounded integrand
unbounded region of integration
increasing
indefinite integral
evaluate
indeterminate form
infinity
inflection point
initial condition
instantaneous rate of change
instantaneous velocity
integral function
integral sign
integrand
integration by parts
left limit
limit
definition
one-sided
limits of integration
local linearization
locally linear
logistic
logistic equation
solution
L’Hôpital’s rule
L’Hôpital’s rule (at infinity)
mass
maximum
absolute
global
local
relative
midpoint rule
error, Item
minimum
absolute
global
local
relative
net signed area
Newton-meter
Newton’s Law of Cooling
one-to-one, Item
onto, Item
partial fractions
per capita growth rate
position
product rule
quotient rule
related rates
Riemann sum
left
middle
right
right limit
secant
secant line
second derivative
second derivative test
second fundamental theorem of calculus
separable
sigma notation
sign chart
Simpson’s rule
slope field
solid of revolution
stable, Item
sum rule
tangent, Item
tangent line
equation
total change theorem
trapezoid rule
error, Item
trigonometry
fundamental trigonometric identity
unstable, Item
washer method
weighted average
work