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E-grāmata: Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice)

Patrick Jones (University of Louisville, KY)

Formāts: PDF+DRM
Izdošanas datums: 21-Apr-2022
Izdevniecība: For Dummies
Valoda: eng
ISBN-13: 9781119883661

Citas grāmatas par šo tēmu:

Calculus & mathematical analysis

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Formāts: PDF+DRM
Izdošanas datums: 21-Apr-2022
Izdevniecība: For Dummies
Valoda: eng
ISBN-13: 9781119883661

Citas grāmatas par šo tēmu:

Calculus & mathematical analysis

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"The perfect companion to Calculus For Dummies...this book offers readers challenging practice problems with step-by-step and detailed answer explanations and narrative walkthroughs. You'll get free access to all 1,001 practice problems online so you cancreate your own study sets for extra-focused learning"--

Practice your way to a higher grade in Calculus!

Calculus is a hands-on skill. You’ve gotta use it or lose it. And the best way to get the practice you need to develop your mathematical talents is Calculus: 1001 Practice Problems For Dummies.

The perfect companion to Calculus For Dummies—and your class— this book offers readers challenging practice problems with step-by-step and detailed answer explanations and narrative walkthroughs. You’ll get free access to all 1,001 practice problems online so you can create your own study sets for extra-focused learning.

Readers will also find:

A useful course supplement and resource for students in high school and college taking Calculus I
Free, one-year access to all practice problems online, for on-the-go study and practice
An excellent preparatory resource for faster-paced college classes

Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) is an essential resource for high school and college students looking for more practice and extra help with this challenging math subject.

Calculus: 1001 Practice Problems For Dummies (9781119883654) was previously published as 1,001 Calculus Practice Problems For Dummies (9781118496718). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Introduction

(4)

What You'll Find

(1)

Beyond the Book

(1)

Where to Go for Additional Help

(3)

PART 1 THE QUESTIONS

(122)

Chapter 1 Algebra Review

(10)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Simplifying Fractions

(1)

Simplifying Radicals

(1)

Writing Exponents Using Radical Notation

(1)

The Horizontal Line Test

(1)

Find Inverses Algebraically

(1)

The Domain and Range of a Function and Its Inverse

(1)

Linear Equations

(1)

Quadratic Equations

(1)

Solving Polynomial Equations by Factoring

(1)

Absolute Value Equations

(1)

Solving Rational Equations

(1)

Polynomial and Rational Inequalities

(1)

Absolute Value Inequalities

(1)

Graphing Common Functions

(1)

Domain and Range from a Graph

(1)

End Behavior of Polynomials

(1)

Adding Polynomials

(1)

Subtracting Polynomials

(1)

Multiplying Polynomials

(1)

Long Division of Polynomials

(1)

Chapter 2 Trigonometry Review

(12)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Basic Trigonometry

(1)

Converting Degree Measure to Radian Measure

(1)

Converting Radian Measure to Degree Measure

(1)

Finding Angles in the Coordinate Plane

(2)

Finding Common Trigonometric Values

(1)

Simplifying Trigonometric Expressions

(1)

Solving Trigonometric Equations

(1)

Amplitude, Period, Phase Shift, and Midline

(1)

Equations of Periodic Functions

(2)

Inverse Trigonometric Function Basics

(1)

Solving Trigonometric Equations Using Inverses

(2)

Chapter 3 Limits and Rates of Change

(14)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Finding Limits from Graphs

(1)

Evaluating Limits

(1)

Applying the Squeeze Theorem

(1)

Evaluating Trigonometric Limits

(1)

Infinite Limits

(3)

Limits from Graphs

(1)

Limits at Infinity

(1)

Horizontal Asymptotes

(1)

Classifying Discontinuities

(1)

Continuity and Discontinuities

(1)

Making a Function Continuous

(1)

The Intermediate Value Theorem

(2)

Chapter 4 Derivative Basics

(6)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Determining Differentiability from a Graph

(1)

Finding the Derivative by Using the Definition

(1)

Finding the Value of the Derivative Using a Graph

(1)

Using the Power Rule to Find Derivatives

(1)

Finding All Points on a Graph Where Tangent Lines Have a Given Value

(1)

Chapter 5 The Product, Quotient, and Chain Rules

(6)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Using the Product Rule to Find Derivatives

(1)

Using the Quotient Rule to Find Derivatives

(2)

Using the Chain Rule to Find Derivatives

(1)

More Challenging Chain Rule Problems

(1)

Chapter 6 Exponential and Logarithmic Functions and Tangent Lines

(4)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Derivatives Involving Logarithmic Functions

(1)

Logarithmic Differentiation to Find the Derivative

(1)

Finding Derivatives of Functions Involving Exponential Functions

(1)

Finding Equations of Tangent Lines

(1)

Finding Equations of Normal Lines

(1)

Chapter 7 Implicit Differentiation

(4)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Using Implicit Differentiation to Find a Derivative

(1)

Using Implicit Differentiation to Find a Second Derivative

(1)

Finding Equations of Tangent Lines Using Implicit Differentiation

(2)

Chapter 8 Applications of Derivatives

(12)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Finding and Evaluating Differentials

(1)

Finding Linearizations

(1)

Using Linearizations to Estimate Values

(1)

Understanding Related Rates

(1)

Finding Maxima and Minima from Graphs

(1)

Using the Closed Interval Method

(1)

Finding Intervals of Increase and Decrease

(1)

Using the First Derivative Test to Find Local Maxima and Minima

(1)

Determining Concavity

(1)

Identifying Inflection Points

(1)

Using the Second Derivative Test to Find Local Maxima and Minima

(1)

Applying Rolle's Theorem

(1)

Using the Mean Value Theorem

(1)

Applying the Mean Value Theorem to Solve Problems

(1)

Relating Velocity and Position

(1)

Finding Velocity and Speed

(1)

Solving Optimization Problems

(1)

Doing Approximations Using Newton's Method

(1)

Approximating Roots Using Newton's Method

(1)

Chapter 9 Areas and Riemann Sums

(4)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Calculating Riemann Sums Using Left Endpoints

(1)

Calculating Riemann Sums Using Right Endpoints

(1)

Calculating Riemann Sums Using Midpoints

(1)

Using Limits and Riemann Sums to Find Expressions for Definite Integrals

(1)

Finding a Definite Integral from the Limit and Riemann Sum Form

(1)

Using Limits and Riemann Sums to Evaluate Definite Integrals

(1)

Chapter 10 The Fundamental Theorem of Calculus and the Net Change Theorem

(8)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Using the Fundamental Theorem of Calculus to Find Derivatives

(1)

Working with Basic Examples of Definite Integrals

(1)

Understanding Basic Indefinite Integrals

(2)

Understanding the Net Change Theorem

(1)

Finding the Displacement of a Particle Given the Velocity

(1)

Finding the Distance Traveled by a Particle Given the Velocity

(1)

Finding the Displacement of a Particle Given Acceleration

(1)

Finding the Distance Traveled by a Particle Given Acceleration

(1)

Chapter 11 Applications of Integration

(14)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Areas between Curves

(1)

Finding Volumes Using Disks and Washers

(2)

Finding Volume Using Cross-Sectional Slices

(1)

Finding Volumes Using Cylindrical Shells

(2)

Work Problems

(4)

Average Value of a Function

(3)

Chapter 12 Inverse Trigonometric Functions, Hyperbolic Functions, and L'Hopital's Rule

101

(8)

The Problems You'll Work On

101

(1)

What to Watch Out For

102

(1)

Finding Derivatives Involving Inverse Trigonometric Functions

102

(1)

Finding Antiderivatives by Using Inverse Trigonometric Functions

103

(1)

Evaluating Hyperbolic Functions Using Their Definitions

104

(1)

Finding Derivatives of Hyperbolic Functions

104

(1)

Finding Antiderivatives of Hyperbolic Functions

105

(1)

Evaluating Indeterminate Forms Using L'Hopital's Rule

105

(4)

Chapter 13 U-Substitution and Integration by Parts

109

(6)

The Problems You'll Work On

109

(1)

What to Watch Out For

109

(1)

Using u-Substitutions

110

(1)

Using Integration by Parts

111

(4)

Chapter 14 Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions

115

(8)

The Problems You'll Work On

115

(1)

What to Watch Out For

116

(1)

Trigonometric Integrals

116

(2)

Trigonometric Substitutions

118

(1)

Finding Partial Fraction Decompositions (without Coefficients)

119

(1)

Finding Partial Fraction Decompositions (Including Coefficients)

120

(1)

Integrals Involving Partial Fractions

120

(1)

Rationalizing Substitutions

121

(2)

Chapter 15 Improper Integrals and More Approximating Techniques

123

(4)

The Problems You'll Work On

123

(1)

What to Watch Out For

123

(1)

Convergent and Divergent Improper Integrals

124

(1)

The Comparison Test for Integrals

125

(1)

The Trapezoid Rule

126

(1)

Simpson's Rule

126

(1)

PART 2 THE ANSWERS

127

(454)

Chapter 16 Answers and Explanations

129

(452)

Index

581

Patrick Jones has a masters degree in Mathematics from the University of Louisville. He has taught at University of Louisville, Vanderbilt University, and Austin Community College. Jones now primarily spends his time expanding his Youtube video library as PatrickJMT.

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