Add Document; Sign In; Register. Calculus, 7th Edition. Home · Calculus, 7th Edition Author: James Stewart. downloads Views 19MB Size Report. James Stewart M c Master University and. University of Toronto Australia • Brazil • Mexico • Singapore • United Kingdom • United States. Calculus 8th edition by James Stewart PDF eTextbook. ISBN Success in your calculus course starts here! James.

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In fact, it can be shown that by taking n large enough that is, by adding sufficiently many terms of the series , we can make the partial sum sn as close as we please to the number 1. Stephanie Kreuz Media Developer: Marketing Channels 7th Edition A Complete Course, 7th. Calculus for the Life Sciences as well as three additional chapters covering probability and statistics. Shopping cart close. For permission to use material from this text or product, submit all requests online at www.

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The Flash simulation modules in TEC include instructions, written and audio explanations of the concepts, and exercises. The meticulously crafted pedagogy and exercises in our proven texts become even more effective in Enhanced WebAssign, supplemented by multimedia tutorial support and immediate feedback as students complete their assignments. Key features include: Instructors can further customize the text by adding instructor-created or YouTube video links.

Additional media assets include animated figures, video clips, highlighting and note-taking features, and more. YouBook is available within Enhanced WebAssign. CourseMate CourseMate is a perfect self-study tool for students, and requires no set up from instructors. CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook.

For instructors, CourseMate includes Engagement Tracker, a first-of-its-kind tool that monitors student engagement. At the CengageBrain. This will take you to the product page where these resources can be found. Cole, and Daniel Drucker ISBN Multivariable By Dan Clegg and Barbara Frank ISBN Provides completely worked-out solutions to all oddnumbered exercises in the text, giving students a chance to check their answer and ensure they took the correct steps to arrive at the answer.

The Student Solutions Manual can be ordered or accessed online as an eBook at www. Andre ISBN For each section of the text, the Study Guide provides students with a brief introduction, a short list of concepts to master, and summary and focus questions with explained answers.

The Study Guide also contains self-tests with exam-style questions. The Study Guide can be ordered or accessed online as an eBook at www. A Companion to Calculus By Dennis Ebersole, Doris Schattschneider, Alicia Sevilla, and Kay Somers ISBN Written to improve algebra and problem-solving skills of students taking a calculus course, every chapter in this companion is keyed to a calculus topic, providing conceptual background and specific algebra techniques needed to understand and solve calculus problems related to that topic.

It is designed for calculus courses that integrate the review of precalculus concepts or for individual use. Order a copy of the text or access the eBook online at www. Linear Algebra for Calculus by Konrad J. Heuvers, William P. Francis, John H. Kuisti, Deborah F. Lockhart, Daniel S. Moak, and Gene M. Ortner ISBN This comprehensive book, designed to supplement the calculus course, provides an introduction to and review of the basic ideas of linear algebra.

To the Student Reading a calculus textbook is different from reading a newspaper or a novel, or even a physics book. You should have pencil and paper and calculator at hand to sketch a diagram or make a calculation.

Some students start by trying their homework problems and read the text only if they get stuck on an exercise. I suggest that a far better plan is to read and understand a section of the text before attempting the exercises.

In particular, you should look at the definitions to see the exact meanings of the terms. And before you read each example, I suggest that you cover up the solution and try solving the problem yourself. Part of the aim of this course is to train you to think logically. Learn to write the solutions of the exercises in a connected, step-by-step fashion with explanatory sentences— not just a string of disconnected equations or formulas.

The answers to the odd-numbered exercises appear at the back of the book, in Appendix H. Some exercises ask for a verbal explanation or interpretation or description. The icon ; indicates an exercise that definitely requires the use of either a graphing calculator or a computer with graphing software. The symbol CAS is reserved for problems in which the full resources of a computer algebra system like Maple, Mathematica, or the TI are required.

You will also encounter the symbol , which warns you against committing an error. I have placed this symbol in the margin in situations where I have observed that a large proportion of my students tend to make the same mistake.

It directs you to modules in which you can explore aspects of calculus for which the computer is particularly useful. You will notice that some exercise numbers are printed in red: This indicates that Homework Hints are available for the exercise. These hints can be found on stewartcalculus. The homework hints ask you questions that allow you to make progress toward a solution without actually giving you the answer.

You need to pursue each hint in an active manner with pencil and paper to work out the details. I recommend that you keep this book for reference purposes after you finish the course. Because you will likely forget some of the specific details of calculus, the book will serve as a useful reminder when you need to use calculus in subsequent courses. And, because this book contains more material than can be covered in any one course, it can also serve as a valuable resource for a working scientist or engineer.

Calculus is an exciting subject, justly considered to be one of the greatest achievements of the human intellect. I hope you will discover that it is not only useful but also intrinsically beautiful.

Similar functionality is available using a web interface at WolframAlpha. Handheld calculators are becoming more powerful, as are software programs and Internet resources. In addition, many mathematical applications have been released for smartphones and tablets such as the iPad. Some exercises in this text are marked with a graphing icon ; , which indicates that the use of some technology is required.

Often this means that we intend for a graphing device to be used in drawing the graph of a function or equation. You might also need technology to find the zeros of a graph or the points of intersection of two graphs. In some cases we will use a calculating device to solve an equation or evaluate a definite integral numerically.

Similar calculators are made by Hewlett Packard, Casio, and Sharp. A CAS is capable of doing mathematics like solving equations, computing derivatives or integrals symbolically rather than just numerically.

Examples of well-established computer algebra systems are the computer software packages Maple and Mathematica. Some tablet and smartphone apps also provide these capabilities, such as the previously mentioned MathStudio. Diagnostic Tests Success in calculus depends to a large extent on knowledge of the mathematics that precedes calculus: The following tests are intended to diagnose weaknesses that you might have in these areas.

After taking each test you can check your answers against the given answers and, if necessary, refresh your skills by referring to the review materials that are provided. Evaluate each expression without using a calculator. Simplify each expression. Write your answer without negative exponents. Expand and simplify. Factor each expression. Simplify the rational expression. Diagnostic Tests xxvii 6. Rationalize the expression and simplify. Rewrite by completing the square.

Solve the equation. Find only the real solutions. Solve each inequality. Write your answer using interval notation. State whether each equation is true or false. Find an equation for the circle that has center s21, 4d and passes through the point s3, 22d. Let As27, 4d and Bs5, d be points in the plane. What are the intercepts?

Sketch the region in the xy-plane defined by the equation or inequalities. Diagnostic Tests xxix C y 1. The graph of a function f is given at the left. Find the domain of the function. How are graphs of the functions obtained from the graph of f?

Without using a calculator, make a rough sketch of the graph. Convert from degrees to radians. Convert from radians to degrees. Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of Find the exact values. Express the lengths a and b in the figure in terms of. Prove the identities. A Preview of Calculus By the time you finish this course, you will be able to calculate the length of the curve used to design the Gateway Arch in St.

Louis, determine where a pilot should start descent for a smooth landing, compute the force on a baseball bat when it strikes the ball, and measure the amount of light sensed by the human eye as the pupil changes size. It is concerned with change and motion; it deals with quantities that approach other quantities.

For that reason it may be useful to have an overview of the subject before beginning its intensive study. Here we give a glimpse of some of the main ideas of calculus by showing how the concept of a limit arises when we attempt to solve a variety of problems. It is a much more difficult problem to find the area of a curved figure. The Greek method of exhaustion was to inscribe polygons in the figure and circumscribe polygons about the figure and then let the number of sides of the polygons increase.

Figure 2 illustrates this process for the special case of a circle with inscribed regular polygons. As n increases, it appears that An becomes closer and closer to the area of the circle.

However, by indirect reasoning, Eudoxus fifth century bc used exhaustion to prove the familiar formula for the area of a circle: We will use a similar idea in Chapter 4 to find areas of regions of the type shown in Figure 3.

We will approximate the desired area A by areas of rectangles as in Figure 4 , let the width of the rectangles decrease, and then calculate A as the limit of these sums of areas of rectangles.

The techniques that we will develop in Chapter 4 for finding areas will also enable us to compute the volume of a solid, the length of a curve, the force of water against a dam, the mass and center of gravity of a rod, and the work done in pumping water out of a tank.

We will give a precise definition of a tangent line in Copyright Cengage Learning. For now you can think of it as a line that touches the curve at P as in Figure 5. Since we know that the point P lies on the tangent line, we can find the equation of t if we know its slope m.

The problem is that we need two points to compute the slope and we know only one point, P, on t.

To get around the problem we first find an approximation to m by taking a nearby point Q on the curve and computing the slope mPQ of the secant line PQ. You can see that the secant line rotates and approaches the tangent line as its limiting position. This means that the slope mPQ of the secant line becomes closer and closer to the slope m of the tangent line.

The tangent problem has given rise to the branch of calculus called differential calculus, which was not invented until more than years after integral calculus. The main ideas behind differential calculus are due to the French mathematician Pierre Fermat — and were developed by the English mathematicians John Wallis — , Isaac Barrow — , and Isaac Newton — and the German mathematician Gottfried Leibniz — The two branches of calculus and their chief problems, the area problem and the tangent problem, appear to be very different, but it turns out that there is a very close connection between them.

The tangent problem and the area problem are inverse problems in a sense that will be described in Chapter 4. Velocity When we look at the speedometer of a car and read that the car is traveling at 48 miyh, what does that information indicate to us?

We know that if the velocity remains constant, then after an hour we will have traveled 48 mi. But if the velocity of the car varies, what does it mean to say that the velocity at a given instant is 48 miyh? Time interval f2, 3g f2, 2. In Chapter 2 we will define the instantaneous velocity of a moving object as the limiting value of the average velocities over smaller and smaller time intervals.

In Figure 8 we show a graphical representation of the motion of the car by plotting the distance traveled as a function of time. The same techniques also enable us to solve problems involving rates of change in all of the natural and social sciences. Zeno argued, as follows, that Achilles could never pass the tortoise: See Figure 9. This process continues indefinitely and so it appears that the tortoise will always be ahead!

But this defies common sense. One way of explaining this paradox is with the idea of a sequence. The successive positions of Achilles sa 1, a 2 , a 3 ,. In general, a sequence ha nj is a set of numbers written in a definite order. For instance, the sequence h1, 12 , 13 , 14 , 15 ,. In fact, we can find terms as small as we please by making n large enough. This means that the numbers a n can be made as close as we like to the number L by taking n sufficiently large. The successive positions of Achilles and the tortoise form sequences ha nj and htn j, where a n , tn for all n.

It can be shown that both sequences have the same limit: In order to do so, he would first have to go half the distance, then half the remaining distance, and then again half of what still remains. This process can always be continued and can never be ended. But there are other situations in which we implicitly use infinite sums.

For instance, in decimal notation, the symbol 0. But we must define carefully what the sum of an infinite series is. Returning to the series in Equation 3, we denote by sn the sum of the first n terms of the series.

In fact, it can be shown that by taking n large enough that is, by adding sufficiently many terms of the series , we can make the partial sum sn as close as we please to the number 1.

Summary We have seen that the concept of a limit arises in trying to find the area of a region, the slope of a tangent to a curve, the velocity of a car, or the sum of an infinite series. In each case the common theme is the calculation of a quantity as the limit of other, easily calculated quantities.

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