# Calculus and Its Applications, 2nd edition

• Marvin L. Bittinger,
• David J. Ellenbogen,
• Scott A. Surgent,
• Gene Kramer

• Search, highlight, notes, and more
• Easily create flashcards
• Use the app for access anywhere
• 14-day refund guarantee

\$10.99per month

Minimum 4-month term, pay monthly or pay \$43.96 upfront

• Watch and learn

Videos & animations bring concepts to life

• Listen on the go

Learn how you like with full eTextbook audio

• Find it fast

Quickly navigate your eTextbook with search

• Stay organized

Access all your eTextbooks in one place

• Easily continue access

Keep learning with auto-renew

## Overview

Calculus and Its Applications is known for an approach that anticipates and meets students' needs, pairing clear explanations with carefully crafted figures to help you visualize concepts. Key revisions in the 2nd Edition include the earlier introduction of logarithmic and exponential functions to help you master these important functions and their applications. New co-author Gene Kramer revisited every homework question and learning aid to improve clarity and accuracy. All aspects of this revision aim to motivate and help students more readily understand and apply calculus principles.

ISBN-13: 9780136880196

Subject: Finite Math & Applied Calculus

Category: Applied Calculus

## Overview

Prerequisite Skills Diagnostic Test

### R. Functions, Graphs, and Models

• R.1 Graphs and Equations
• R.2 Functions and Models
• R.3 Finding Domain and Range
• R.4 Slope and Linear Functions
• R.5 Nonlinear Functions and Models
• R.6 Exponential and Logarithmic Functions
• R.7 Mathematical Modeling and Curve Fitting
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Average Price of a Movie Ticket

### 1. Differentiation

• 1.1 Limits: A Numerical and Graphical Approach
• 1.2 Algebraic Limits and Continuity
• 1.3 Average Rates of Change
• 1.4 Differentiation Using Limits and Difference Quotients
• 1.5 Leibniz Notation and the Power and Sum–Difference Rules
• 1.6 The Product and Quotient Rules
• 1.7 The Chain Rule
• 1.8 Higher-Order Derivatives
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Path of a Baseball: The Tale of the Tape

### 2. Exponential and Logarithmic Functions

• 2.1 Exponential and Logarithmic Functions of the Natural Base, e
• 2.2 Derivatives of Exponential (Base-e) Functions
• 2.3 Derivatives of Natural Logarithmic Functions
• 2.4 Applications: Uninhibited and Limited Growth Models
• 2.5 Applications: Exponential Decay
• 2.6 The Derivatives of ax and loga x
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: The Business of Motion Picture Revenue and DVD Release

### 3. Applications of Differentiation

• 3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
• 3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
• 3.3 Graph Sketching: Asymptotes and Rational Functions
• 3.4 Optimization: Finding Absolute Maximum and Minimum Values
• 3.5 Optimization: Business, Economics, and General Applications
• 3.6 Marginals, Differentials, and Linearization
• 3.7 Elasticity of Demand
• 3.8 Implicit Differentiation and Logarithmic Differentiation
• 3.9 Related Rates
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Maximum Sustainable Harvest

### 4. Integration

• 4.1 Antidifferentiation
• 4.2 Antiderivatives as Areas
• 4.3 Area and Definite Integrals
• 4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average
• 4.5 Integration Techniques: Substitution
• 4.6 Integration Techniques: Integration by Parts
• 4.7 Numerical Integration
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Business and Economics: Distribution of Wealth

### 5. Applications of Integration

• 5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss
• 5.2 Integrating Growth and Decay Models
• 5.3 Improper Integrals
• 5.4 Probability
• 5.5 Probability: Expected Value; the Normal Distribution
• 5.6 Volume
• 5.7 Differential Equations
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Curve Fitting and Volumes of Containers

### 6. Functions of Several Variables

• 6.1 Functions of Several Variables
• 6.2 Partial Derivatives
• 6.3 Maximum–Minimum Problems
• 6.4 An Application: The Least-Squares Technique
• 6.5 Constrained Optimization: Lagrange Multipliers and the Extreme-Value Theorem
• 6.6 Double Integrals
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application: Minimizing Employees' Travel Time in a Building

### 7. Trigonometric Functions

• 7.1 Basics of Trigonometry
• 7.2 Derivatives of Trigonometric Functions
• 7.3 Integration of Trigonometric Functions
• 7.4 Inverse Trigonometric Functions and Applications
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application

### 8. Differential Equations

• 8.1 Direction Fields, Autonomic Forms, and Population Models
• 8.2 Applications: Inhibited Growth Models
• 8.3 First-Order Linear Differential Equations
• 8.4 Higher-Order Differential Equations and a Trigonometry Connection
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application

### 9. Sequences and Series

• 9.1 Arithmetic Sequences and Series
• 9.2 Geometric Sequences and Series
• 9.3 Simple and Compound Interest
• 9.4 Annuities and Amortization
• 9.5 Power Series and Linearization
• 9.6 Taylor Series and a Trigonometry Connection
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application

### 10. Probability Distributions

• 10.1 A Review of Sets
• 10.2 Theoretical Probability
• 10.3 Discrete Probability Distributions
• 10.4 Continuous Probability Distributions: Mean, Variance, and Standard Deviation
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application

### 11. Systems and Matrices (online only)

• 11.1 Systems of Linear Equations
• 11.2 Gaussian Elimination
• 11.3 Matrices and Row Operations
• 11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples
• 11.5 Matrix Multiplication, Multiplicative Identities, and Inverses
• 11.6 Determinants and Cramer's Rule
• 11.7 Systems of Linear Inequalities and Linear Programming
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application

### 12. Combinatorics and Probability (online only)

• 12.1 Compound Events and Odds
• 12.2 Combinatorics: The Multiplication Principle and Factorial Notation
• 12.3 Permutations and Distinguishable Arrangements
• 12.4 Combinations and the Binomial Theorem
• 12.5 Conditional Probability and the Hypergeometric Probability Distribution Model
• 12.6 Independent Events, Bernoulli Trials, and the Binomial Probability Model
• 12.7 Bayes Theorem
• Chapter Summary
• Chapter Review Exercises
• Chapter Test
• Extended Technology Application
• Cumulative Review

### Appendices

1. Review of Basic Algebra
2. Indeterminate Forms and l'Hôpital's Rule
3. Regression and Microsoft Excel
4. Areas for a Standard Normal Distribution
5. Using Tables of Integration Formulas

#### Index

Pearson+ is your one-stop shop, with eTextbooks and study videos designed to help students get better grades in college.
A Pearson eTextbook is an easy‑to‑use digital version of the book. You'll get upgraded study tools, including enhanced search, highlights and notes, flashcards and audio. Plus learn on the go with the Pearson+ app.
Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.

When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.

If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.

To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.

Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.
When you choose a Channels subscription, you're signing up for a 1‑month, 3‑month or 12‑month term and you make an upfront payment for your subscription. By default, these subscriptions auto‑renew at the frequency you select during checkout.

When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.