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1001 Calculus Practice Problems for Dummies by PatrickJMT



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1001 Calculus Practice Problems for Dummies written by PatrickJMT. cover the following topics.

  • Introduction
    What You’ll Find
    Beyond the Book.1
    What you’ll find online
    How to register
    Where to Go for Additional Help

  • Part I: The Questions

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 11: Applications of Integration
    The Problems You’ll Work O
    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

  • 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

  • 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

  • 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

  • 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

  • 16: Answers and Explanations

  • Index

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