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

by Jones, Patrick

• ISBN13: 9781119883654
• ISBN10: 1119883652
• Edition: 1st
• Format: Paperback
• Copyright: 2022-06-01
• Publisher: For Dummies

Summary

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.

Author Biography

Patrick Jones has a master’s 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.

Table of Contents

Introduction 1

What You’ll Find 1

Beyond the Book 2

Where to Go for Additional Help 2

Part 1: The Questions 5

Chapter 1: Algebra Review 7

The Problems You’ll Work On 7

What to Watch Out For 7

Simplifying Fractions 8

Simplifying Radicals 8

Writing Exponents Using Radical Notation 9

The Horizontal Line Test 9

Find Inverses Algebraically 10

The Domain and Range of a Function and Its Inverse 10

Linear Equations 10

Quadratic Equations 11

Solving Polynomial Equations by Factoring 11

Absolute Value Equations 12

Solving Rational Equations 12

Polynomial and Rational Inequalities 12

Absolute Value Inequalities 13

Graphing Common Functions 13

Domain and Range from a Graph 14

End Behavior of Polynomials 15

Adding Polynomials 15

Subtracting Polynomials 15

Multiplying Polynomials 16

Long Division of Polynomials 16

Chapter 2: Trigonometry Review 17

The Problems You’ll Work On 17

What to Watch Out For 17

Basic Trigonometry 18

Converting Degree Measure to Radian Measure 18

Converting Radian Measure to Degree Measure 19

Finding Angles in the Coordinate Plane 19

Finding Common Trigonometric Values 21

Simplifying Trigonometric Expressions 21

Solving Trigonometric Equations 22

Amplitude, Period, Phase Shift, and Midline 23

Equations of Periodic Functions 24

Inverse Trigonometric Function Basics 26

Solving Trigonometric Equations Using Inverses 27

Chapter 3: Limits and Rates of Change 29

The Problems You’ll Work On 29

What to Watch Out For 29

Finding Limits from Graphs 30

Evaluating Limits 31

Applying the Squeeze Theorem 32

Evaluating Trigonometric Limits 33

Infinite Limits 33

Limits from Graphs 36

Limits at Infinity 37

Horizontal Asymptotes 38

Classifying Discontinuities 38

Continuity and Discontinuities 39

Making a Function Continuous 40

The Intermediate Value Theorem 41

Chapter 4: Derivative Basics 43

The Problems You’ll Work On 43

What to Watch Out For 43

Determining Differentiability from a Graph 44

Finding the Derivative by Using the Definition 45

Finding the Value of the Derivative Using a Graph 46

Using the Power Rule to Find Derivatives 47

Finding All Points on a Graph Where Tangent Lines Have a Given Value 48

Chapter 5: The Product, Quotient, and Chain Rules 49

The Problems You’ll Work On 49

What to Watch Out For 49

Using the Product Rule to Find Derivatives 50

Using the Quotient Rule to Find Derivatives 51

Using the Chain Rule to Find Derivatives 53

More Challenging Chain Rule Problems 54

Chapter 6: Exponential and Logarithmic Functions and Tangent Lines 55

The Problems You’ll Work On 55

What to Watch Out For 55

Derivatives Involving Logarithmic Functions 56

Logarithmic Differentiation to Find the Derivative 56

Finding Derivatives of Functions Involving Exponential Functions 57

Finding Equations of Tangent Lines 58

Finding Equations of Normal Lines 58

Chapter 7: Implicit Differentiation 59

The Problems You’ll Work On 59

What to Watch Out For 59

Using Implicit Differentiation to Find a Derivative 60

Using Implicit Differentiation to Find a Second Derivative 60

Finding Equations of Tangent Lines Using Implicit Differentiation 61

Chapter 8: Applications of Derivatives 63

The Problems You’ll Work On 63

What to Watch Out For 63

Finding and Evaluating Differentials 64

Finding Linearizations 64

Using Linearizations to Estimate Values 64

Understanding Related Rates 65

Finding Maxima and Minima from Graphs 66

Using the Closed Interval Method 67

Finding Intervals of Increase and Decrease 68

Using the First Derivative Test to Find Local Maxima and Minima 68

Determining Concavity 69

Identifying Inflection Points 69

Using the Second Derivative Test to Find Local Maxima and Minima 69

Applying Rolle’s Theorem 70

Using the Mean Value Theorem 70

Applying the Mean Value Theorem to Solve Problems 70

Relating Velocity and Position 71

Finding Velocity and Speed 71

Solving Optimization Problems 72

Doing Approximations Using Newton’s Method 73

Approximating Roots Using Newton’s Method 74

Chapter 9: Areas and Riemann Sums 75

The Problems You’ll Work On 75

What to Watch Out For 75

Calculating Riemann Sums Using Left Endpoints 76

Calculating Riemann Sums Using Right Endpoints 76

Calculating Riemann Sums Using Midpoints 77

Using Limits and Riemann Sums to Find Expressions for Definite Integrals 77

Finding a Definite Integral from the Limit and Riemann Sum Form 78

Using Limits and Riemann Sums to Evaluate Definite Integrals 78

Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem 79

The Problems You’ll Work On 79

What to Watch Out For 80

Using the Fundamental Theorem of Calculus to Find Derivatives 80

Working with Basic Examples of Definite Integrals 81

Understanding Basic Indefinite Integrals 82

Understanding the Net Change Theorem 84

Finding the Displacement of a Particle Given the Velocity 85

Finding the Distance Traveled by a Particle Given the Velocity 85

Finding the Displacement of a Particle Given Acceleration 86

Finding the Distance Traveled by a Particle Given Acceleration 86

Chapter 11: Applications of Integration 87

The Problems You’ll Work On 87

What to Watch Out For 87

Areas between Curves 88

Finding Volumes Using Disks and Washers 89

Finding Volume Using Cross-Sectional Slices 91

Finding Volumes Using Cylindrical Shells 92

Work Problems 94

Average Value of a Function 98

Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions, and L’Hôpital’s Rule 101

The Problems You’ll Work On 101

What to Watch Out For 102

Finding Derivatives Involving Inverse Trigonometric Functions 102

Finding Antiderivatives by Using Inverse Trigonometric Functions 103

Evaluating Hyperbolic Functions Using Their Definitions 104

Finding Derivatives of Hyperbolic Functions 104

Finding Antiderivatives of Hyperbolic Functions 105

Evaluating Indeterminate Forms Using L’Hôpital’s Rule 105

Chapter 13: U-Substitution and Integration by Parts 109

The Problems You’ll Work On 109

What to Watch Out For 109

Using u-Substitutions 110

Using Integration by Parts 111

Chapter 14: Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions 115

The Problems You’ll Work On 115

What to Watch Out For 116

Trigonometric Integrals 116

Trigonometric Substitutions 118

Finding Partial Fraction Decompositions (without Coefficients) 119

Finding Partial Fraction Decompositions (Including Coefficients) 120

Integrals Involving Partial Fractions 120

Rationalizing Substitutions 121

Chapter 15: Improper Integrals and More Approximating Techniques 123

The Problems You’ll Work On 123

What to Watch Out For 123

Convergent and Divergent Improper Integrals 124

The Comparison Test for Integrals 125

The Trapezoid Rule 126

Simpson’s Rule 126

Part 2: The Answers 127

Chapter 16: Answers and Explanations 129

Index 581