A

absolute extremum4.3 Maxima and Minima

absolute maximum4.3 Maxima and Minima

absolute minimum4.3 Maxima and Minima

absolute value function1.1 Review of Functions

algebraic function1.2 Basic Classes of Functions

amount of change3.4 Derivatives as Rates of Change

antiderivative4.10 Antiderivatives

area density6.5 Physical Applications

Area Problem2.1 A Preview of Calculus

area under the curve5.1 Approximating Areas

average rate of change3.4 Derivatives as Rates of Change

average value of the function5.2 The Definite Integral

B

C

carbon dating6.8 Exponential Growth and Decay

center of mass6.6 Moments and Centers of Mass

centroid6.6 Moments and Centers of Mass

chain rule3.6 The Chain Rule

change of variables5.5 Substitution

chaos4.9 Newton’s Method

common logarithm1.5 Exponential and Logarithmic Functions

composite function1.1 Review of Functions

compound interest6.8 Exponential Growth and Decay

compounding interest1.5 Exponential and Logarithmic Functions

concave down4.5 Derivatives and the Shape of a Graph

concave up4.5 Derivatives and the Shape of a Graph

concavity test4.5 Derivatives and the Shape of a Graph

conditional statement2.5 The Precise Definition of a Limit

constant function1.2 Basic Classes of Functions

Constant multiple law for limits2.3 The Limit Laws

Constant Multiple Rule3.3 Differentiation Rules

constant rule3.3 Differentiation Rules

continuity over an interval2.4 Continuity

continuous at a point2.4 Continuity

continuous from the left2.4 Continuity

continuous from the right2.4 Continuity

critical point4.3 Maxima and Minima

cross-section6.2 Determining Volumes by Slicing

cubic function1.2 Basic Classes of Functions

D

decreasing on the interval II1.1 Review of Functions

definite integral5.2 The Definite Integral

density function6.5 Physical Applications

dependent variable1.1 Review of Functions

derivative3.1 Defining the Derivative

derivative function3.2 The Derivative as a Function

Difference law for limits2.3 The Limit Laws

difference quotient3.1 Defining the Derivative

Difference Rule3.3 Differentiation Rules

differentiable at aa3.2 The Derivative as a Function

differentiable function3.2 The Derivative as a Function

differentiable on SS3.2 The Derivative as a Function

Differential calculus2.1 A Preview of Calculus

differential form4.2 Linear Approximations and Differentials

differentials4.2 Linear Approximations and Differentials

differentiation3.1 Defining the Derivative

discontinuous at a point2.4 Continuity

disk method6.2 Determining Volumes by Slicing

domain1.1 Review of Functions

doubling time6.8 Exponential Growth and Decay

E

endpoints1.1 Review of Functions

epsilon-delta definition of the limit2.5 The Precise Definition of a Limit

evaluation theorem5.3 The Fundamental Theorem of Calculus

existential quantifier2.5 The Precise Definition of a Limit

exponential decay6.8 Exponential Growth and Decay

exponential growth6.8 Exponential Growth and Decay

Extreme Value Theorem4.3 Maxima and Minima

F

federal income tax5.4 Integration Formulas and the Net Change Theorem

Fermat’s theorem4.3 Maxima and Minima

first derivative test4.5 Derivatives and the Shape of a Graph

folium of Descartes3.8 Implicit Differentiation

function1.1 Review of Functions

Fundamental Theorem of Calculus5.3 The Fundamental Theorem of Calculus

Fundamental Theorem of Calculus, Part 15.3 The Fundamental Theorem of Calculus

Fundamental Theorem of Calculus, Part 25.3 The Fundamental Theorem of Calculus

G

graph of a function1.1 Review of Functions

growth of bacteria5.6 Integrals Involving Exponential and Logarithmic Functions

H

half-life6.8 Exponential Growth and Decay

hanging cables6.9 Calculus of the Hyperbolic Functions

higher-order derivatives3.2 The Derivative as a Function

Holling type I equation3.4 Derivatives as Rates of Change

Hooke’s law6.5 Physical Applications

Hoover Dam6.5 Physical Applications

horizontal asymptote4.6 Limits at Infinity and Asymptotes

horizontal line test1.4 Inverse Functions

hydrostatic pressure6.5 Physical Applications

hyperbolic functions1.5 Exponential and Logarithmic Functions

I

implicit differentiation3.8 Implicit Differentiation

increasing on the interval II1.1 Review of Functions

indefinite integral4.10 Antiderivatives

independent variable1.1 Review of Functions

indeterminate forms4.8 L’Hôpital’s Rule

infinite discontinuity2.4 Continuity

infinite limit at infinity4.6 Limits at Infinity and Asymptotes

infinite limits2.2 The Limit of a Function

inflection point4.5 Derivatives and the Shape of a Graph

initial-value problem4.10 Antiderivatives

instantaneous rate of change3.1 Defining the Derivative

integrable function5.2 The Definite Integral

Integral calculus2.1 A Preview of Calculus

integrand5.2 The Definite Integral

integration by substitution5.5 Substitution

interior points3.2 The Derivative as a Function

Intermediate Value Theorem2.4 Continuity

interval notation1.1 Review of Functions

intuitive definition of the limit2.2 The Limit of a Function

inverse function1.4 Inverse Functions

inverse hyperbolic functions1.5 Exponential and Logarithmic Functions

inverse trigonometric functions1.4 Inverse Functions

iterative process4.9 Newton’s Method

L

L’Hôpital’s rule4.8 L’Hôpital’s Rule

leading coefficient1.2 Basic Classes of Functions

left-endpoint approximation5.1 Approximating Areas

limit laws2.3 The Limit Laws

limits of integration5.2 The Definite Integral

linear approximation4.2 Linear Approximations and Differentials

linear function1.2 Basic Classes of Functions

linearization4.2 Linear Approximations and Differentials

local extremum4.3 Maxima and Minima

local maximum4.3 Maxima and Minima

local minimum4.3 Maxima and Minima

logarithmic differentiation3.9 Derivatives of Exponential and Logarithmic Functions

logarithmic function1.2 Basic Classes of Functions

lower sum5.1 Approximating Areas

M

Mandelbrot set4.9 Newton’s Method

marginal cost3.4 Derivatives as Rates of Change

marginal profit3.4 Derivatives as Rates of Change

mathematical models1.2 Basic Classes of Functions

maximizing revenue4.7 Applied Optimization Problems

Mean Value Theorem4.4 The Mean Value Theorem

Mean Value Theorem for Integrals5.3 The Fundamental Theorem of Calculus

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

method of exhaustion5.1 Approximating Areas

multivariable calculus2.1 A Preview of Calculus

N

natural exponential function1.5 Exponential and Logarithmic Functions, 3.9 Derivatives of Exponential and Logarithmic Functions

natural logarithm1.5 Exponential and Logarithmic Functions

natural logarithmic function3.9 Derivatives of Exponential and Logarithmic Functions

net change theorem5.4 Integration Formulas and the Net Change Theorem

net signed area5.2 The Definite Integral

Newton’s law of cooling6.8 Exponential Growth and Decay

Newton’s method4.9 Newton’s Method

O

oblique asymptote4.6 Limits at Infinity and Asymptotes

one-sided limit2.2 The Limit of a Function

one-to-one function1.4 Inverse Functions

optimization problems4.7 Applied Optimization Problems

output1.1 Review of Functions

P

partition5.1 Approximating Areas

Pascal’s principle6.5 Physical Applications

pascals6.5 Physical Applications

percentage error4.2 Linear Approximations and Differentials

perihelion5.3 The Fundamental Theorem of Calculus

periodic functions.1.3 Trigonometric Functions

piecewise-defined function1.2 Basic Classes of Functions

piecewise-defined functions1.1 Review of Functions

point-slope equation1.2 Basic Classes of Functions

polynomial function1.2 Basic Classes of Functions

population growth rates3.4 Derivatives as Rates of Change

power function1.2 Basic Classes of Functions

Power law for limits2.3 The Limit Laws

power rule3.3 Differentiation Rules

price–demand function5.6 Integrals Involving Exponential and Logarithmic Functions

Product law for limits2.3 The Limit Laws

product rule3.3 Differentiation Rules

propagated error4.2 Linear Approximations and Differentials

Pythagorean theorem4.1 Related Rates

Q

quadratic function1.2 Basic Classes of Functions

Quotient law for limits2.3 The Limit Laws

quotient rule3.3 Differentiation Rules

R

radial density6.5 Physical Applications

radians1.3 Trigonometric Functions

rational function1.2 Basic Classes of Functions

Regiomontanus’ problem4.10 Antiderivatives

regular partition5.1 Approximating Areas

related rates4.1 Related Rates

relative error4.2 Linear Approximations and Differentials

removable discontinuity2.4 Continuity

restricted domain1.4 Inverse Functions

Richter scale1.5 Exponential and Logarithmic Functions

Riemann sum5.1 Approximating Areas

right-endpoint approximation5.1 Approximating Areas

Rolle’s theorem4.4 The Mean Value Theorem

root function1.2 Basic Classes of Functions

Root law for limits2.3 The Limit Laws

S

secant method4.9 Newton’s Method

second derivative test4.5 Derivatives and the Shape of a Graph

sigma notation5.1 Approximating Areas

simple interest6.8 Exponential Growth and Decay

slicing method6.2 Determining Volumes by Slicing

slope-intercept form1.2 Basic Classes of Functions

solid of revolution6.2 Determining Volumes by Slicing

spring constant6.5 Physical Applications

squeeze theorem2.3 The Limit Laws

standard form of a line1.2 Basic Classes of Functions

Sum law for limits2.3 The Limit Laws

Sum Rule3.3 Differentiation Rules

summation notation5.1 Approximating Areas

sums and powers of integers5.1 Approximating Areas

Surface area6.4 Arc Length of a Curve and Surface Area

symmetry about the origin1.1 Review of Functions

symmetry about the y-axis1.1 Review of Functions

symmetry principle6.6 Moments and Centers of Mass

T

table of values1.1 Review of Functions

tangent2.1 A Preview of Calculus

tangent line approximation4.2 Linear Approximations and Differentials

Tangent Problem2.1 A Preview of Calculus

theorem of Pappus for volume6.6 Moments and Centers of Mass

total area5.2 The Definite Integral

Tour de France5.4 Integration Formulas and the Net Change Theorem

transcendental functions1.2 Basic Classes of Functions

transformation of a function1.2 Basic Classes of Functions

triangle inequality2.5 The Precise Definition of a Limit

trigonometric functions1.3 Trigonometric Functions

trigonometric identity1.3 Trigonometric Functions

V

variable of integration5.2 The Definite Integral

vertical asymptote2.2 The Limit of a Function

vertical line test1.1 Review of Functions

W

washer method6.2 Determining Volumes by Slicing