1001 calculus practice problems for dummies

Title Page
Copyright Page
Contents at a Glance
Table of Contents
Introduction
	What You’ll Find
	Beyond the Book
	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 Function Basics
		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
		Logarithmic Differentiation to Find the Derivative
		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
		Doing Approximations Using Newton’s Method
		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
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