1,001 Calculus Practice Problems For Dummies

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Table of Contents
Course Details

Algebra Review

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

Trigonometry Review

Basic Trigonometry

Converting Degree Measure to Radian Measure

Converting Radian Measure to Degree Measure

Finding Angles in the Coordinate Plane

Finding Common Trigonometric Values

Amplitude, Period, Phase Shift, and Midline

Equations of Periodic Functions

Inverse Trigonometric Function Basics

Solving Trigonometric Equations Using Inverses

Limits and Rates of Change

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

Derivative Basics

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

The Product, Quotient, and Chain Rule

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

Exponential and Logarithmic Functions and Tangent Lines

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

Implicit Differentiation

Using Implicit Differentiation to Find a Derivative

Using Implicit Differentiation to Find a Second Derivative

Finding Equations of Tangent Lines Using Implicit Differentiation

Applications of Derivatives

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

Areas and Riemann Sums

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

The Fundamental Theorem of Calculus and the Net Change Theorem

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

Applications of Integration

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

Inverse Trigonometric Functions, Hyperbolic Functions, and L'Hôpital's Rule

Finding Derivatives Involving Inverse Trigonometric Functions

Finding Antiderivatives by Using Inverse Trigonometric Functions

Evaluating Hyperbolic Functions Using Their Definitions

Finding the Derivative of Functions Involving Hyperbolic Functions

Finding Antiderivatives of Functions Involving Hyperbolic Functions

Evaluating Indeterminate Forms Using L'Hôpital's Rule

-Substitution and Integration by Parts

Using u-Substitutions

Using Integration by Parts

Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions

Trigonometric Integrals

Trigonometric Substitutions

Finding Partial Fraction Decompositions (without Coefficients)

Finding Partial Fraction Decompositions (Including Coefficients)

Integrals Involving Partial Fractions

Rationalizing Substitutions

Improper Integrals and More Approximating Techniques

Convergent and Divergent Improper Integrals

The Comparison Test for Integrals

The Trapezoid Rule

Simpson's Rule

Description:

This powerful online resource offers 1,001 practice problems that will help you get a handle on calculus. You'll find review questions on algebra and trigonometry to get you started, and then you can move on to derivatives, logarithmic functions, differentiation, the fundamental theorem of calculus, and much more. All practice problems include answers and step-by-step solutions. These problems—categorized as easy, medium, and hard—let you track your progress, see what you need to study most, and then create customized question sets to get you where you need to be.