A

absolute extremum
4.3 Maxima and Minima

absolute maximum
4.3 Maxima and Minima

absolute minimum
4.3 Maxima and Minima

absolute value function
1.1 Review of Functions

algebraic function
1.2 Basic Classes of Functions

amount of change
3.4 Derivatives as Rates of Change

antiderivative
4.10 Antiderivatives

arc length
6.4 Arc Length of a Curve and Surface Area

*area density*6.5 Physical Applications

Area Problem
2.1 A Preview of Calculus

area under the curve
5.1 Approximating Areas

average rate of change
3.4 Derivatives as Rates of Change

average value of the function
5.2 The Definite Integral

B

C

carbon dating
6.8 Exponential Growth and Decay

center of mass
6.6 Moments and Centers of Mass

centroid
6.6 Moments and Centers of Mass

chain rule
3.6 The Chain Rule

change of variables
5.5 Substitution

chaos
4.9 Newton’s Method

*common logarithm*1.5 Exponential and Logarithmic Functions

composite function
1.1 Review of Functions

compound interest
6.8 Exponential Growth and Decay

compounding interest
1.5 Exponential and Logarithmic Functions

concave down
4.5 Derivatives and the Shape of a Graph

concave up
4.5 Derivatives and the Shape of a Graph

concavity
4.5 Derivatives and the Shape of a Graph

concavity test
4.5 Derivatives and the Shape of a Graph

*conditional statement*2.5 The Precise Definition of a Limit

*constant function*1.2 Basic Classes of Functions

Constant multiple law for limits
2.3 The Limit Laws

Constant Multiple Rule
3.3 Differentiation Rules

constant rule
3.3 Differentiation Rules

continuity over an interval
2.4 Continuity

continuous at a point
2.4 Continuity

continuous from the left
2.4 Continuity

continuous from the right
2.4 Continuity

critical number
4.3 Maxima and Minima

cross-section
6.2 Determining Volumes by Slicing

cubic function
1.2 Basic Classes of Functions

D

deceleration
5.4 Integration Formulas and the Net Change Theorem

decreasing on the interval
$I$
1.1 Review of Functions

definite integral
5.2 The Definite Integral

density function
6.5 Physical Applications

dependent variable
1.1 Review of Functions

derivative
3.1 Defining the Derivative

derivative function
3.2 The Derivative as a Function

Difference law for limits
2.3 The Limit Laws

difference quotient
3.1 Defining the Derivative

Difference Rule
3.3 Differentiation Rules

differentiable at
$a$
3.2 The Derivative as a Function

differentiable function
3.2 The Derivative as a Function

differentiable on
$S$
3.2 The Derivative as a Function

Differential calculus
2.1 A Preview of Calculus

differential form
4.2 Linear Approximations and Differentials

differentials
4.2 Linear Approximations and Differentials

differentiation
3.1 Defining the Derivative

discontinuous at a point
2.4 Continuity

disk method
6.2 Determining Volumes by Slicing

domain
1.1 Review of Functions

doubling time
6.8 Exponential Growth and Decay

E

earthquake
1.5 Exponential and Logarithmic Functions

*endpoints*1.1 Review of Functions

epsilon-delta definition of the limit
2.5 The Precise Definition of a Limit

evaluation theorem
5.3 The Fundamental Theorem of Calculus

*existential quantifier*2.5 The Precise Definition of a Limit

exponential decay
6.8 Exponential Growth and Decay

exponential growth
6.8 Exponential Growth and Decay

Extreme Value Theorem
4.3 Maxima and Minima

F

*f*

_{ave}5.2 The Definite Integral

federal income tax
5.4 Integration Formulas and the Net Change Theorem

Fermat’s theorem
4.3 Maxima and Minima

first derivative test
4.5 Derivatives and the Shape of a Graph

folium of Descartes
3.8 Implicit Differentiation

function
1.1 Review of Functions

Fundamental Theorem of Calculus
5.3 The Fundamental Theorem of Calculus

Fundamental Theorem of Calculus, Part 1
5.3 The Fundamental Theorem of Calculus

Fundamental Theorem of Calculus, Part 2
5.3 The Fundamental Theorem of Calculus

G

graph of a function
1.1 Review of Functions

growth of bacteria
5.6 Integrals Involving Exponential and Logarithmic Functions

H

half-life
6.8 Exponential Growth and Decay

hanging cables
6.9 Calculus of the Hyperbolic Functions

higher-order derivatives
3.2 The Derivative as a Function

Holling type I equation
3.4 Derivatives as Rates of Change

Hooke’s law
6.5 Physical Applications

Hoover Dam
6.5 Physical Applications

horizontal asymptote
4.6 Limits at Infinity and Asymptotes

horizontal line test
1.4 Inverse Functions

hydrostatic pressure
6.5 Physical Applications

hyperbolic functions
1.5 Exponential and Logarithmic Functions

I

implicit differentiation
3.8 Implicit Differentiation

increasing on the interval
$I$
1.1 Review of Functions

indefinite integral
4.10 Antiderivatives

independent variable
1.1 Review of Functions

indeterminate forms
4.8 L’Hôpital’s Rule

*index*5.1 Approximating Areas

infinite discontinuity
2.4 Continuity

infinite limit at infinity
4.6 Limits at Infinity and Asymptotes

infinite limits
2.2 The Limit of a Function

inflection point
4.5 Derivatives and the Shape of a Graph

initial-value problem
4.10 Antiderivatives

*input*1.1 Review of Functions

instantaneous rate of change
3.1 Defining the Derivative

integrable function
5.2 The Definite Integral

Integral calculus
2.1 A Preview of Calculus

integrand
5.2 The Definite Integral

integration by substitution
5.5 Substitution

interior points
3.2 The Derivative as a Function

Intermediate Value Theorem
2.4 Continuity

interval notation
1.1 Review of Functions

intuitive definition of the limit
2.2 The Limit of a Function

inverse function
1.4 Inverse Functions

inverse hyperbolic functions
1.5 Exponential and Logarithmic Functions

inverse trigonometric functions
1.4 Inverse Functions

iterative process
4.9 Newton’s Method

L

L’Hôpital’s rule
4.8 L’Hôpital’s Rule

*leading coefficient*1.2 Basic Classes of Functions

left-endpoint approximation
5.1 Approximating Areas

limit laws
2.3 The Limit Laws

limits of integration
5.2 The Definite Integral

linear approximation
4.2 Linear Approximations and Differentials

linear function
1.2 Basic Classes of Functions

linearization
4.2 Linear Approximations and Differentials

local extremum
4.3 Maxima and Minima

local maximum
4.3 Maxima and Minima

local minimum
4.3 Maxima and Minima

logarithmic differentiation
3.9 Derivatives of Exponential and Logarithmic Functions

logarithmic function
1.2 Basic Classes of Functions

lower sum
5.1 Approximating Areas

M

Mandelbrot set
4.9 Newton’s Method

marginal cost
3.4 Derivatives as Rates of Change

marginal profit
3.4 Derivatives as Rates of Change

mathematical models
1.2 Basic Classes of Functions

maximizing revenue
4.7 Applied Optimization Problems

Mean Value Theorem
4.4 The Mean Value Theorem

Mean Value Theorem for Integrals
5.3 The Fundamental Theorem of Calculus

method of cylindrical shells.
6.3 Volumes of Revolution: Cylindrical Shells

*method of exhaustion*5.1 Approximating Areas

multivariable calculus
2.1 A Preview of Calculus

N

natural exponential function
1.5 Exponential and Logarithmic Functions,
3.9 Derivatives of Exponential and Logarithmic Functions

natural logarithm
1.5 Exponential and Logarithmic Functions

natural logarithmic function
3.9 Derivatives of Exponential and Logarithmic Functions

net change theorem
5.4 Integration Formulas and the Net Change Theorem

net signed area
5.2 The Definite Integral

Newton’s law of cooling
6.8 Exponential Growth and Decay

Newton’s method
4.9 Newton’s Method

number
$e$
1.5 Exponential and Logarithmic Functions

O

oblique asymptote
4.6 Limits at Infinity and Asymptotes

one-sided limit
2.2 The Limit of a Function

one-to-one function
1.4 Inverse Functions

optimization problems
4.7 Applied Optimization Problems

*output*1.1 Review of Functions

P

partition
5.1 Approximating Areas

Pascal’s principle
6.5 Physical Applications

*pascals*6.5 Physical Applications

percentage error
4.2 Linear Approximations and Differentials

*perihelion*5.3 The Fundamental Theorem of Calculus

periodic functions.
1.3 Trigonometric Functions

piecewise-defined function
1.2 Basic Classes of Functions

*piecewise-defined functions*1.1 Review of Functions

point-slope equation
1.2 Basic Classes of Functions

polynomial function
1.2 Basic Classes of Functions

population growth rates
3.4 Derivatives as Rates of Change

power function
1.2 Basic Classes of Functions

Power law for limits
2.3 The Limit Laws

power rule
3.3 Differentiation Rules

price–demand function
5.6 Integrals Involving Exponential and Logarithmic Functions

Product law for limits
2.3 The Limit Laws

product rule
3.3 Differentiation Rules

propagated error
4.2 Linear Approximations and Differentials

Pythagorean theorem
4.1 Related Rates

Q

quadratic function
1.2 Basic Classes of Functions

Quotient law for limits
2.3 The Limit Laws

quotient rule
3.3 Differentiation Rules

R

*radial density*6.5 Physical Applications

radians
1.3 Trigonometric Functions

range
1.1 Review of Functions

rational function
1.2 Basic Classes of Functions

Regiomontanus’ problem
4 Review Exercises

regular partition
5.1 Approximating Areas

related rates
4.1 Related Rates

relative error
4.2 Linear Approximations and Differentials

removable discontinuity
2.4 Continuity

restricted domain
1.4 Inverse Functions

*Richter scale*1.5 Exponential and Logarithmic Functions

Riemann sum
5.1 Approximating Areas

right-endpoint approximation
5.1 Approximating Areas

Rolle’s theorem
4.4 The Mean Value Theorem

root function
1.2 Basic Classes of Functions

Root law for limits
2.3 The Limit Laws

S

secant
2.1 A Preview of Calculus

secant method
4.9 Newton’s Method

second derivative test
4.5 Derivatives and the Shape of a Graph

sigma notation
5.1 Approximating Areas

*simple interest*6.8 Exponential Growth and Decay

slicing method
6.2 Determining Volumes by Slicing

slope-intercept form
1.2 Basic Classes of Functions

solid of revolution
6.2 Determining Volumes by Slicing

*spring constant*6.5 Physical Applications

squeeze theorem
2.3 The Limit Laws

standard form of a line
1.2 Basic Classes of Functions

Sum law for limits
2.3 The Limit Laws

Sum Rule
3.3 Differentiation Rules

summation notation
5.1 Approximating Areas

sums and powers of integers
5.1 Approximating Areas

Surface area
6.4 Arc Length of a Curve and Surface Area

symmetry about the origin
1.1 Review of Functions

symmetry about the

*y*-axis 1.1 Review of Functions
symmetry principle
6.6 Moments and Centers of Mass

T

table of values
1.1 Review of Functions

tangent
2.1 A Preview of Calculus

tangent line approximation
4.2 Linear Approximations and Differentials

Tangent Problem
2.1 A Preview of Calculus

theorem of Pappus for volume
6.6 Moments and Centers of Mass

total area
5.2 The Definite Integral

Tour de France
5.4 Integration Formulas and the Net Change Theorem

transcendental functions
1.2 Basic Classes of Functions

transformation of a function
1.2 Basic Classes of Functions

triangle inequality
2.5 The Precise Definition of a Limit

trigonometric functions
1.3 Trigonometric Functions

trigonometric identity
1.3 Trigonometric Functions

V

variable of integration
5.2 The Definite Integral

vertical asymptote
2.2 The Limit of a Function

vertical line test
1.1 Review of Functions

W

washer method
6.2 Determining Volumes by Slicing

wingsuits
5.3 The Fundamental Theorem of Calculus