Math 2.0

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Active Calculus 907G4C4EJ1

URIm2://res/907G4C4EJ1
Kindtextbook
CreatorsMatthew Boelkins, David Austin, Steven Schlicker
Date2026-10-26
MSC26A06
Scopein

Expressions

e1: edition

Languageen
Date2026-10-26
Contents
  • chapter 1: Understanding the Derivative
  • section 1.1: How do we measure velocity?
  • subsection 1.1.1: Introduction
  • subsection 1.1.2: Position and average velocity
  • subsection 1.1.3: Instantaneous Velocity
  • subsection 1.1.4: Summary
  • section 1.2: The notion of limit
  • subsection 1.2.1: Introduction
  • subsection 1.2.2: The Notion of Limit
  • subsection 1.2.3: Instantaneous Velocity
  • subsection 1.2.4: Summary
  • section 1.3: The derivative of a function at a point
  • subsection 1.3.1: Introduction
  • subsection 1.3.2: The Derivative of a Function at a Point
  • subsection 1.3.3: Summary
  • section 1.4: The derivative function
  • subsection 1.4.1: Introduction
  • subsection 1.4.2: How the derivative is itself a function
  • subsection 1.4.3: Summary
  • section 1.5: Interpreting, estimating, and using the derivative
  • subsection 1.5.1: Introduction
  • subsection 1.5.2: Units of the derivative function
  • subsection 1.5.3: Toward more accurate derivative estimates
  • subsection 1.5.4: Summary
  • section 1.6: The second derivative
  • subsection 1.6.1: Introduction
  • subsection 1.6.2: Increasing or decreasing
  • subsection 1.6.3: The Second Derivative
  • subsection 1.6.4: Concavity
  • subsection 1.6.5: Summary
  • section 1.7: Limits, continuity, and differentiability
  • subsection 1.7.1: Introduction
  • subsection 1.7.2: Having a limit at a point
  • subsection 1.7.3: Being continuous at a point
  • subsection 1.7.4: Being differentiable at a point
  • subsection 1.7.5: Summary
  • section 1.8: The tangent line approximation
  • subsection 1.8.1: Introduction
  • subsection 1.8.2: The tangent line
  • subsection 1.8.3: The local linearization
  • subsection 1.8.4: Summary
  • chapter 2: Computing Derivatives
  • section 2.1: Elementary derivative rules
  • subsection 2.1.1: Introduction
  • subsection 2.1.2: Some Key Notation
  • subsection 2.1.3: Constant, Power, and Exponential Functions
  • subsection 2.1.4: Constant Multiples and Sums of Functions
  • subsection 2.1.5: Summary
  • section 2.2: The sine and cosine functions
  • subsection 2.2.1: Introduction
  • subsection 2.2.2: The sine and cosine functions
  • subsection 2.2.3: Summary
  • section 2.3: The product and quotient rules
  • subsection 2.3.1: Introduction
  • subsection 2.3.2: The product rule
  • subsection 2.3.3: The quotient rule
  • subsection 2.3.4: Combining rules
  • subsection 2.3.5: Summary
  • section 2.4: Derivatives of other trigonometric functions
  • subsection 2.4.1: Introduction
  • subsection 2.4.2: Derivatives of the cotangent, secant, and cosecant functions
  • subsection 2.4.3: Summary
  • section 2.5: The chain rule
  • subsection 2.5.1: Introduction
  • subsection 2.5.2: The chain rule
  • subsection 2.5.3: Using multiple rules simultaneously
  • subsection 2.5.4: The composite version of basic function rules
  • subsection 2.5.5: Summary
  • section 2.6: Derivatives of inverse functions
  • subsection 2.6.1: Introduction
  • subsection 2.6.2: Basic facts about inverse functions
  • subsection 2.6.3: The derivative of the natural logarithm function
  • subsection 2.6.4: Inverse trigonometric functions and their derivatives
  • subsection 2.6.5: The link between the derivative of a function and the derivative of its inverse
  • subsection 2.6.6: Summary
  • section 2.7: Derivatives of functions given implicitly
  • subsection 2.7.1: Introduction
  • subsection 2.7.2: Implicit Differentiation
  • subsection 2.7.3: Summary
  • chapter 3: Using Derivatives
  • section 3.1: Related rates
  • subsection 3.1.1: Introduction
  • subsection 3.1.2: Related Rates Problems
  • subsection 3.1.3: Summary
  • section 3.2: Using derivatives to evaluate limits
  • subsection 3.2.1: Introduction
  • subsection 3.2.2: Using derivatives to evaluate indeterminate limits of the form $\frac{0}{0}$.
  • subsection 3.2.3: Limits involving $\infty$
  • subsection 3.2.4: Summary
  • section 3.3: Using derivatives to identify extreme values
  • subsection 3.3.1: Introduction
  • subsection 3.3.2: Critical numbers and the first derivative test
  • subsection 3.3.3: The second derivative test
  • subsection 3.3.4: Summary
  • section 3.4: Using derivatives to describe families of functions
  • subsection 3.4.1: Introduction
  • subsection 3.4.2: Describing families of functions in terms of parameters
  • subsection 3.4.3: Summary
  • section 3.5: Global optimization
  • subsection 3.5.1: Introduction
  • subsection 3.5.2: Global Optimization
  • subsection 3.5.3: Moving toward applications
  • subsection 3.5.4: Summary
  • section 3.6: Applied optimization
  • subsection 3.6.1: Introduction
  • subsection 3.6.2: More applied optimization problems
  • subsection 3.6.3: Summary
  • chapter 4: The Definite Integral
  • section 4.1: Determining distance traveled from velocity
  • subsection 4.1.1: Introduction
  • subsection 4.1.2: Area under the graph of the velocity function
  • subsection 4.1.3: Two approaches: area and antidifferentiation
  • subsection 4.1.4: When velocity is negative
  • subsection 4.1.5: Summary
  • section 4.2: Riemann sums
  • subsection 4.2.1: Introduction
  • subsection 4.2.2: Sigma Notation
  • subsection 4.2.3: Riemann Sums
  • subsection 4.2.4: When the function is sometimes negative
  • subsection 4.2.5: Summary
  • section 4.3: The definite integral
  • subsection 4.3.1: Introduction
  • subsection 4.3.2: The definition of the definite integral
  • subsection 4.3.3: Some properties of the definite integral
  • subsection 4.3.4: How the definite integral is connected to a function's average value
  • subsection 4.3.5: Summary
  • section 4.4: The Fundamental Theorem of Calculus
  • subsection 4.4.1: Introduction
  • subsection 4.4.2: The Fundamental Theorem of Calculus
  • subsection 4.4.3: Basic antiderivatives
  • subsection 4.4.4: The total change theorem
  • subsection 4.4.5: Summary
  • chapter 5: Evaluating Integrals
  • section 5.1: Constructing accurate graphs of antiderivatives
  • subsection 5.1.1: Introduction
  • subsection 5.1.2: Constructing the graph of an antiderivative
  • subsection 5.1.3: Multiple antiderivatives of a single function
  • subsection 5.1.4: Functions defined by integrals
  • subsection 5.1.5: Summary
  • section 5.2: The Second Fundamental Theorem of Calculus
  • subsection 5.2.1: Introduction
  • subsection 5.2.2: The Second Fundamental Theorem of Calculus
  • subsection 5.2.3: Understanding Integral Functions
  • subsection 5.2.4: Differentiating an Integral Function
  • subsection 5.2.5: Summary
  • section 5.3: Integration by substitution
  • subsection 5.3.1: Introduction
  • subsection 5.3.2: Reversing the Chain Rule: First Steps
  • subsection 5.3.3: Reversing the Chain Rule: $u$-substitution
  • subsection 5.3.4: Evaluating Definite Integrals via $u$-substitution
  • subsection 5.3.5: Summary
  • section 5.4: Integration by parts
  • subsection 5.4.1: Introduction
  • subsection 5.4.2: Reversing the Product Rule: Integration by Parts
  • subsection 5.4.3: Some Subtleties with Integration by Parts
  • subsection 5.4.4: Using Integration by Parts Multiple Times
  • subsection 5.4.5: Evaluating Definite Integrals Using Integration by Parts
  • subsection 5.4.6: When $u$-substitution and Integration by Parts Fail to Help
  • subsection 5.4.7: Summary
  • section 5.5: Other options for finding algebraic antiderivatives
  • subsection 5.5.1: Introduction
  • subsection 5.5.2: The Method of Partial Fractions
  • subsection 5.5.3: Using an Integral Table
  • subsection 5.5.4: Using Computer Algebra Systems
  • subsection 5.5.5: Summary
  • section 5.6: Numerical integration
  • subsection 5.6.1: Introduction
  • subsection 5.6.2: The Trapezoid Rule
  • subsection 5.6.3: Comparing the Midpoint and Trapezoid Rules
  • subsection 5.6.4: Simpson's Rule
  • subsection 5.6.5: Overall observations regarding $L_n$, $R_n$, $T_n$, $M_n$, and $S_{2n}$.
  • subsection 5.6.6: Summary
  • chapter 6: Using Definite Integrals
  • section 6.1: Using definite integrals to find area and length
  • subsection 6.1.1: Introduction
  • subsection 6.1.2: The Area Between Two Curves
  • subsection 6.1.3: Finding Area with Horizontal Slices
  • subsection 6.1.4: Finding the length of a curve
  • subsection 6.1.5: Summary
  • section 6.2: Using definite integrals to find volume
  • subsection 6.2.1: Introduction
  • subsection 6.2.2: The Volume of a Solid of Revolution
  • subsection 6.2.3: Revolving about the $y$-axis
  • subsection 6.2.4: Revolving about horizontal and vertical lines other than the coordinate axes
  • subsection 6.2.5: Summary
  • section 6.3: Density, mass, and center of mass
  • subsection 6.3.1: Introduction
  • subsection 6.3.2: Density
  • subsection 6.3.3: Weighted Averages
  • subsection 6.3.4: Center of Mass
  • subsection 6.3.5: Summary
  • section 6.4: Physics applications: work, force, and pressure
  • subsection 6.4.1: Introduction
  • subsection 6.4.2: Work
  • subsection 6.4.3: Work: Pumping Liquid from a Tank
  • subsection 6.4.4: Force due to Hydrostatic Pressure
  • subsection 6.4.5: Summary
  • section 6.5: Improper integrals
  • subsection 6.5.1: Introduction
  • subsection 6.5.2: Improper Integrals Involving Unbounded Intervals
  • subsection 6.5.3: Convergence and Divergence
  • subsection 6.5.4: Improper Integrals Involving Unbounded Integrands
  • subsection 6.5.5: Summary
  • chapter 7: Differential Equations
  • section 7.1: An introduction to differential equations
  • subsection 7.1.1: Introduction
  • subsection 7.1.2: What is a differential equation?
  • subsection 7.1.3: Differential equations in the world around us
  • subsection 7.1.4: Solving a differential equation
  • subsection 7.1.5: Summary
  • section 7.2: Qualitative behavior of solutions to differential equations
  • subsection 7.2.1: Introduction
  • subsection 7.2.2: Slope fields
  • subsection 7.2.3: Equilibrium solutions and stability
  • subsection 7.2.4: Summary
  • section 7.3: Euler's method
  • subsection 7.3.1: Introduction
  • subsection 7.3.2: Euler's Method
  • subsection 7.3.3: The error in Euler's method
  • subsection 7.3.4: Summary
  • section 7.4: Separable differential equations
  • subsection 7.4.1: Introduction
  • subsection 7.4.2: Solving separable differential equations
  • subsection 7.4.3: Summary
  • section 7.5: Modeling with differential equations
  • subsection 7.5.1: Introduction
  • subsection 7.5.2: Developing a differential equation
  • subsection 7.5.3: Summary
  • section 7.6: Population growth and the logistic equation
  • subsection 7.6.1: Introduction
  • subsection 7.6.2: The earth's population
  • subsection 7.6.3: Solving the logistic differential equation
  • subsection 7.6.4: Summary
  • appendix A: A Short Table of Integrals

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

ItemKindWhereSource
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washer methodconceptindex, section 6.2.2active_calculus
Newton-meterconceptindex, section 6.4.1active_calculus
equilibrium solutionconceptindex, section 7.2.3active_calculus
second derivativeconceptindex, section 1.6.3active_calculus
$u$-substitutionconceptindex, section 5.3.3active_calculus
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derivative, exponential functionconceptindex, section 2.1.3active_calculus
concave downconceptindex, section 1.6.4active_calculus
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densityconceptindex, section 6.3.2active_calculus
Time as a function of speedexampleexample, section 1.5.2active_calculus
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locally linearconceptindex, section 1.7.4active_calculus
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maximum, absoluteconceptindex, section 3.3.1active_calculus
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sign chartconceptindex, section 3.3.2active_calculus
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critical pointconceptindex, section 3.3.2active_calculus
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function-derivative pairconceptindex, section 5.3.3active_calculus
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total change theoremconceptindex, section 4.4.4active_calculus
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partial fractionsconceptindex, section 5.5.2active_calculus
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definite integral, sum ruleconceptindex, section 4.3.3active_calculus
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logistic equation, solutionconceptindex, section 7.6.3active_calculus
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quotient ruleconceptindex, section 2.3.3active_calculus
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massconceptindex, section 6.3.2active_calculus
secant lineconceptindex, section 1.3.2active_calculus
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instantaneous rate of changeconceptindex, section 1.3.2active_calculus
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weighted averageconceptindex, section 5.6.4active_calculus
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asymptote, horizontalconceptindex, section 3.2.3active_calculus
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backward differenceconceptindex, section 1.5.3active_calculus
integral functionconceptindex, section 5.1.4active_calculus
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differentiableconceptindex, section 1.7.4active_calculus
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differential equation, first orderconceptindex, section 7.1.4active_calculus
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trapezoid rule, errorconceptindex, section 5.6.2active_calculus
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difference quotientconceptindex, section 1.5.3active_calculus
areaconceptindex, section 6.1.2active_calculus
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average valueconceptindex, section 4.3.4active_calculus
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CEC6GSFBS6exerciseactivity, section 1.5.3active_calculus
CHDADK5A1Gexerciseactivity, section 7.3.2active_calculus
Euler's Method, errorconceptindex, section 7.3.3active_calculus
CKPQ6NHJGTexampleexample, section 2.3.3active_calculus
center of mass (continuous mass distribution)conceptindex, section 6.3.4active_calculus
continuousconceptindex, section 1.7.3active_calculus
CVRV296GYVexerciseactivity, section 1.3.2active_calculus
Riemann sum, middleconceptindex, section 4.2.3active_calculus
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tangent lineconceptindex, section 1.3.2active_calculus
DAVD7SBNEAexerciseactivity, section 1.7.3active_calculus
net signed areaconceptindex, section 4.2.4active_calculus
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equilibrium solution, stableconceptindex, section 7.2.3active_calculus
Riemann sum, leftconceptindex, section 4.2.3active_calculus
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first derivative testconceptindex, section 3.3.2active_calculus
constant multiple ruleconceptindex, section 2.1.4active_calculus
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center of mass (point-massesconceptindex, section 6.3.4active_calculus
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derivative, inverseconceptindex, section 2.6.5active_calculus
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average velocityconceptindex, section 1.1.4active_calculus
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positionconceptindex, section 1.1.2active_calculus
derivative, logarithmconceptindex, section 2.6.3active_calculus
trigonometryconceptindex, section 2.4.1active_calculus
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Limits of Two Functionsexampleexample, section 1.2.2active_calculus
increasingconceptindex, section 1.6.1active_calculus
critical valueconceptindex, section 3.3.2active_calculus
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tangentconceptindex, section 2.4.1active_calculus
slope fieldconceptindex, section 7.2.2active_calculus
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extreme value theoremconceptindex, section 3.5.2active_calculus
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arc lengthconceptindex, section 6.1.4active_calculus
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logisticconceptindex, section 7.6.3active_calculus
M8MVCBRPMRexerciseactivity, section 2.4.2active_calculus
derivative, constant functionconceptindex, section 2.1.3active_calculus
MB8E91N5CKexerciseactivity, section 4.3.4active_calculus
MFBQC5EES1exampleexample, section 6.1.3active_calculus
indefinite integralconceptindex, section 5.3.2active_calculus
MXMJWY79YMexampleexample, section 2.1.3active_calculus
concavityconceptindex, section 1.6.4active_calculus
second fundamental theorem of calculusconceptindex, section 5.2.2active_calculus
N68PFXJQP5exerciseactivity, section 2.4.2active_calculus
error functionconceptindex, section 5.5.4active_calculus
asymptote, verticalconceptindex, section 3.2.3active_calculus
N8Y08TYKCYexerciseactivity, section 5.2.2active_calculus
N8YJQVZ6GEdefinitiondefinition, section 1.3.2active_calculus
N9MFVDTH6Yexerciseactivity, section 2.6.4active_calculus
antidifferentiationconceptindex, section 4.1.3active_calculus
NF0XNMBS2Qexerciseactivity, section 7.3.2active_calculus
NKBPJW1MMPdefinitiondefinition, section 4.3.2active_calculus
extreme valueconceptindex, section 3.3.1active_calculus
accelerationconceptindex, section 1.6.4active_calculus
NWCEAZ769Texerciseactivity, section 2.3.4active_calculus
trapezoid ruleconceptindex, section 5.6.2active_calculus
NX88K7YMJWexampleexample, section 2.5.2active_calculus
minimum, globalconceptindex, section 3.3.1active_calculus
arcsineconceptindex, section 2.6.4active_calculus
P1QJD1BVBFexerciseactivity, section 7.4.2active_calculus
P2BWFFT2HRexerciseactivity, section 3.4.2active_calculus
P40YBECARTexerciseactivity, section 5.3.2active_calculus
improper integralconceptindex, section 6.5.2active_calculus
second derivative testconceptindex, section 3.3.3active_calculus
P9WVEDBQTBexampleexample, section 2.5.2active_calculus
limit, definitionconceptindex, section 1.2.2active_calculus
compositionconceptindex, section 2.5.1active_calculus
PJZ99S9KDFexerciseactivity, section 2.3.3active_calculus
domainconceptindex, section 2.6.2active_calculus
Euler's Methodconceptindex, section 7.3.2active_calculus
Q38CYSVT19definitiondefinition, section 1.3.1active_calculus
related ratesconceptindex, section 3.1.2active_calculus
cosecantconceptindex, section 2.4.2active_calculus
left limitconceptindex, section 1.7.2active_calculus
QJNQMXC48Bexampleexample, section 2.5.4active_calculus
QKMZ7WPKFEexerciseactivity, section 6.5.3active_calculus
QPEZN5GQYVexerciseactivity, section 5.6.4active_calculus
QQ730RJ7RMexerciseactivity, section 3.3.3active_calculus
QRDB451Y4Zexampleexample, section 2.5.1active_calculus
QVMF4GSG2Zexerciseactivity, section 4.3.2active_calculus
solid of revolutionconceptindex, section 6.2.2active_calculus
functionconceptindex, section 2.6.2active_calculus
R381X2B7C9exerciseactivity, section 6.1.3active_calculus
decreasingconceptindex, section 1.6.1active_calculus
antiderivative, graphconceptindex, section 5.1.2active_calculus
Fundamental Theorem of Calculus, Secondconceptindex, section 5.2.2active_calculus
one-to-oneconceptindex, section 2.6.2active_calculus
differential equation, solutionconceptindex, section 7.1.4active_calculus
RS6ZRA08ECexerciseactivity, section 7.1.3active_calculus
distance traveledconceptindex, section 4.1.3active_calculus
separableconceptindex, section 7.4.2active_calculus
autonomousconceptindex, section 7.1.4active_calculus
cuspconceptindex, section 1.7.4active_calculus
carrying capacityconceptindex, section 7.6.3active_calculus
SFV37NW3NTexampleexample, section 5.5.2active_calculus
SG14CEHTHHexerciseactivity, section 4.2.4active_calculus
SG1N9ZZEJ3exerciseactivity, section 6.5.4active_calculus
error functionconceptindex, section 5.2.3active_calculus
asymptoteconceptindex, section 3.2.3active_calculus
FTCconceptindex, section 4.4.2active_calculus
tangent line, equationconceptindex, section 1.8.2active_calculus
fundamental theorem of calculusconceptindex, section 4.4.2active_calculus
SRETEFVGBQexerciseactivity, section 6.2.2active_calculus
critical numberconceptindex, section 3.3.2active_calculus
derivative, sineconceptindex, section 2.2.2active_calculus
SVG0R7Z0T5exampleexample, section 2.1.4active_calculus
codomainconceptindex, section 2.6.2active_calculus
instantaneous rate of changeconceptindex, section 1.5.2active_calculus
Simpson's ruleconceptindex, section 5.6.4active_calculus
TECD7DCNWQexerciseactivity, section 1.6.4active_calculus
TEEHP37JD6exampleexample, section 2.7.2active_calculus
Population growthexampleexample, section 1.5.2active_calculus
TGXV7JRZYRexerciseactivity, section 3.3.3active_calculus
per capita growth rateconceptindex, section 7.6.2active_calculus
THYCPSTRRDexerciseactivity, section 2.7.2active_calculus
TJ5P4F6G30exerciseactivity, section 3.6.2active_calculus
TN47ZA03MJexerciseactivity, section 5.1.2active_calculus
TNS1Q3M73Texerciseactivity, section 3.5.2active_calculus
cotangentconceptindex, section 2.4.2active_calculus
instantaneous velocityconceptindex, section 1.1.3active_calculus
V1VGE2Z1QMexerciseactivity, section 5.4.3active_calculus
V3DWB4JF02exampleexample, section 7.4.2active_calculus
VABQVMVE10exerciseactivity, section 4.1.2active_calculus
limits of integrationconceptindex, section 4.3.2active_calculus
indeterminate formconceptindex, section 1.2.2active_calculus
VCSEGYXAS5exerciseactivity, section 3.5.2active_calculus
VN131QM26Zexampleexample, section 7.5.2active_calculus
VNSBW7JH6Mexerciseactivity, section 6.3.2active_calculus
improper integral, convergesconceptindex, section 6.5.3active_calculus
W4BC5QFN9Vexerciseactivity, section 1.8.3active_calculus
W7Q8K9MRWZexerciseactivity, section 5.3.3active_calculus
Using the limit definition of the derivativeexampleexample, section 1.3.2active_calculus
workconceptindex, section 6.4.1active_calculus
antiderivative, generalconceptindex, section 4.4.3active_calculus
WJ01FTBB8Bexerciseactivity, section 7.5.2active_calculus
WMWJS768FWexampleexample, section 5.4.2active_calculus
integration by partsconceptindex, section 5.4.2active_calculus
WQB98YY9QEexampleexample, section 3.2.3active_calculus
WSNMA19GMFexerciseactivity, section 2.2.2active_calculus
WTTEBS2376exerciseactivity, section 1.5.2active_calculus
area, under velocity functionconceptindex, section 4.1.2active_calculus
foot-poundconceptindex, section 6.4.1active_calculus
WZAT5WHY83exerciseactivity, section 6.1.2active_calculus
midpoint rule, errorconceptindex, section 5.6.2active_calculus
X0B2RT6TT7exampleexample, section 6.2.3active_calculus
infinityconceptindex, section 3.2.3active_calculus
minimum, relativeconceptindex, section 3.3.1active_calculus
definite integral, definitionconceptindex, section 4.3.2active_calculus
X8M8P5CQQWexerciseactivity, section 2.1.4active_calculus
XB3AJZSDRNexerciseactivity, section 6.1.4active_calculus
integral signconceptindex, section 4.3.2active_calculus
XG1K213F14exampleexample, section 3.3.2active_calculus
XHTNC0D9FHexerciseactivity, section 5.6.2active_calculus
XR82KTQ3CGdefinitiondefinition, section 1.7.2active_calculus
XR922XJGVCdefinitiondefinition, section 1.6.4active_calculus
XTXQXV1FYNexerciseactivity, section 3.1.2active_calculus
XW3NKJ17CMexerciseactivity, section 5.4.4active_calculus
logistic equationconceptindex, section 7.6.3active_calculus
disk methodconceptindex, section 6.2.2active_calculus
Y0KBQ416B0exerciseactivity, section 3.6.2active_calculus
Y2ZSA8MA6Eexerciseactivity, section 2.6.3active_calculus
Y4AYW6YCNTexerciseactivity, section 3.3.2active_calculus
average rate of changeconceptindex, section 1.3.1active_calculus
inflection pointconceptindex, section 3.3.3active_calculus
Y96F0E73HXexerciseactivity, section 1.2.3active_calculus
stableconceptindex, section 7.2.3active_calculus
folium of Descartesconceptindex, section 2.7.1active_calculus
right limitconceptindex, section 1.7.2active_calculus
Riemann sumconceptindex, section 4.2.3active_calculus
limit, one-sidedconceptindex, section 1.7.2active_calculus
Z9PJKGX3VDdefinitiondefinition, section 1.5.3active_calculus
trigonometry, fundamental trigonometric identityconceptindex, section 2.4.1active_calculus
ZFKFDJYM1Xexerciseactivity, section 7.1.2active_calculus
derivative, cosineconceptindex, section 2.2.2active_calculus
ZK5KQ9PW9Yexerciseactivity, section 2.3.2active_calculus
minimum, absoluteconceptindex, section 3.3.1active_calculus
ZRBCWS5NKFexerciseactivity, section 4.2.3active_calculus
ZSG3YDRV70exerciseactivity, section 2.2.2active_calculus
ZVKCSX7HDAexerciseactivity, section 3.6.2active_calculus
ZXQ22RAKGFexerciseactivity, section 3.2.2active_calculus

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