Calculus, 1001 Practice Problems For Dummies - PatrickJMT

Introduction

What You’ll Find

Beyond the Book

What You’ll Find Online

How to Register

Where to Go for Additional Help

Part I: The Questions

Chapter 1: 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

Chapter 2: 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 Functions

Solving Trigonometric Equations Using Inverses

Chapter 3: 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

Chapter 4: 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

Chapter 5: 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

Chapter 6: Exponential and Logarithmic Functions and Tangent Lines

The Problems You’ll Work On

What to Watch Out For

Derivatives Involving Logarithmic Functions

Finding Derivatives of Functions Involving Exponential Functions

Finding Equations of Tangent Lines

Finding Equations of Normal Lines

Chapter 7: 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

Chapter 8: 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

Approximating Roots Using Newton’s Method

Chapter 9: 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

Chapter 10: 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

Chapter 11: 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

Chapter 12: 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

Chapter 13: U-Substitution and Integration by Parts

The Problems You’ll Work On

What to Watch Out For

Using u-Substitutions

Using Integration by Parts

Chapter 14: 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

Chapter 15: 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

Part II: The Answers

Chapter 16: Answers and Explanations

Index