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Patrick Jones. Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice)
Calculus: 1001 Practice Problems For Dummies® To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Calculus: 1001 Practice Problems For Dummies Cheat Sheet” in the Search box. Table of Contents
Guide
Pages
Introduction
What You’ll Find
Beyond the Book
Where to Go for Additional Help
The Questions
Algebra Review
The Problems You’ll Work On
What to Watch Out For
Simplifying Fractions
Simplifying Radicals
Writing Exponents Using Radical Notation
The Horizontal Line Test
Find Inverses Algebraically
The Domain and Range of a Function and Its Inverse
Linear Equations
Quadratic Equations
Solving Polynomial Equations by Factoring
Absolute Value Equations
Solving Rational Equations
Polynomial and Rational Inequalities
Absolute Value Inequalities
Graphing Common Functions
Domain and Range from a Graph
End Behavior of Polynomials
Adding Polynomials
Subtracting Polynomials
Multiplying Polynomials
Long Division of Polynomials
Trigonometry Review
The Problems You’ll Work On
What to Watch Out For
Basic Trigonometry
Converting Degree Measure to Radian Measure
Converting Radian Measure to Degree Measure
Finding Angles in the Coordinate Plane
Finding Common Trigonometric Values
Simplifying Trigonometric Expressions
Solving Trigonometric Equations
Amplitude, Period, Phase Shift, and Midline
Equations of Periodic Functions
Inverse Trigonometric Function Basics
Solving Trigonometric Equations Using Inverses
Limits and Rates of Change
The Problems You’ll Work On
What to Watch Out For
Finding Limits from Graphs
Evaluating Limits
Applying the Squeeze Theorem
Evaluating Trigonometric Limits
Infinite Limits
Limits from Graphs
Limits at Infinity
Horizontal Asymptotes
Classifying Discontinuities
Continuity and Discontinuities
Making a Function Continuous
The Intermediate Value Theorem
Derivative Basics
The Problems You’ll Work On
What to Watch Out For
Determining Differentiability from a Graph
Finding the Derivative by Using the Definition
Finding the Value of the Derivative Using a Graph
Using the Power Rule to Find Derivatives
Finding All Points on a Graph Where Tangent Lines Have a Given Value
The Product, Quotient, and Chain Rules
The Problems You’ll Work On
What to Watch Out For
Using the Product Rule to Find Derivatives
Using the Quotient Rule to Find Derivatives
Using the Chain Rule to Find Derivatives
More Challenging Chain Rule Problems
Exponential and Logarithmic Functions and Tangent Lines
The Problems You’ll Work On
What to Watch Out For
Derivatives Involving Logarithmic Functions
Logarithmic Differentiation to Find the Derivative
Finding Derivatives of Functions Involving Exponential Functions
Finding Equations of Tangent Lines
Finding Equations of Normal Lines
Implicit Differentiation
The Problems You’ll Work On
What to Watch Out For
Using Implicit Differentiation to Find a Derivative
Using Implicit Differentiation to Find a Second Derivative
Finding Equations of Tangent Lines Using Implicit Differentiation
Applications of Derivatives
The Problems You’ll Work On
What to Watch Out For
Finding and Evaluating Differentials
Finding Linearizations
Using Linearizations to Estimate Values
Understanding Related Rates
Finding Maxima and Minima from Graphs
Using the Closed Interval Method
Finding Intervals of Increase and Decrease
Using the First Derivative Test to Find Local Maxima and Minima
Determining Concavity
Identifying Inflection Points
Using the Second Derivative Test to Find Local Maxima and Minima
Applying Rolle’s Theorem
Using the Mean Value Theorem
Applying the Mean Value Theorem to Solve Problems
Relating Velocity and Position
Finding Velocity and Speed
Solving Optimization Problems
Doing Approximations Using Newton’s Method
Approximating Roots Using Newton’s Method
Areas and Riemann Sums
The Problems You’ll Work On
What to Watch Out For
Calculating Riemann Sums Using Left Endpoints
Calculating Riemann Sums Using Right Endpoints
Calculating Riemann Sums Using Midpoints
Using Limits and Riemann Sums to Find Expressions for Definite Integrals
Finding a Definite Integral from the Limit and Riemann Sum Form
Using Limits and Riemann Sums to Evaluate Definite Integrals
The Fundamental Theorem of Calculus and the Net Change Theorem
The Problems You’ll Work On
What to Watch Out For
Using the Fundamental Theorem of Calculus to Find Derivatives
Working with Basic Examples of Definite Integrals
Understanding Basic Indefinite Integrals
Understanding the Net Change Theorem
Finding the Displacement of a Particle Given the Velocity
Finding the Distance Traveled by a Particle Given the Velocity
Finding the Displacement of a Particle Given Acceleration
Finding the Distance Traveled by a Particle Given Acceleration
Applications of Integration
The Problems You’ll Work On
What to Watch Out For
Areas between Curves
Finding Volumes Using Disks and Washers
Finding Volume Using Cross-Sectional Slices
Finding Volumes Using Cylindrical Shells
Work Problems
Average Value of a Function
Inverse Trigonometric Functions, Hyperbolic Functions, and L'Hôpital's Rule
The Problems You’ll Work On
What to Watch Out For
Finding Derivatives Involving Inverse Trigonometric Functions
Finding Antiderivatives by Using Inverse Trigonometric Functions
Evaluating Hyperbolic Functions Using Their Definitions
Finding Derivatives of Hyperbolic Functions
Finding Antiderivatives of Hyperbolic Functions
Evaluating Indeterminate Forms Using L'Hôpital's Rule
U-Substitution and Integration by Parts
The Problems You’ll Work On
What to Watch Out For
Using u-Substitutions
Using Integration by Parts
Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions
The Problems You’ll Work On
What to Watch Out For
Trigonometric Integrals
Trigonometric Substitutions
Finding Partial Fraction Decompositions (without Coefficients)
Finding Partial Fraction Decompositions (Including Coefficients)
Integrals Involving Partial Fractions
Rationalizing Substitutions
Improper Integrals and More Approximating Techniques
The Problems You’ll Work On
What to Watch Out For
Convergent and Divergent Improper Integrals
The Comparison Test for Integrals
The Trapezoid Rule
Simpson’s Rule
The Answers
Answers and Explanations
Index. A
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
About the Author
Author’s Acknowledgments
WILEY END USER LICENSE AGREEMENT
