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For those distance functions, the speed (the slope) is continually changing. If we divide the total distance by the total time, we only know one number: the average speed. What calculus finds is the speed at each separate moment—the whole history of speed from the whole history of distance.
Introduction to Calculus. 1.1 Velocity and Distance. The right way to begin a calculus book is with calculus. This chapter will jump directly into the two problems that the subject was invented to solve. You will see what the questions are, and you will see an important part of the answer.
This collection of solved problems covers elementary and intermediate calculus, and much of advanced calculus. We have aimed at presenting the broadest range of problems that you are likely to encounter—the old chestnuts, all the current standard types, and some not so standard. Each chapter begins with very elementary problems.
It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor’s Manual and a student Study Guide. The complete textbook (PDF) is also available as a single file.
Consult our compendium of more than 20 calculus books in PDF, available for free and immediate download. Here we present our complete selection of Calculus books: Calculus Volume 1
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Study calculus online free by downloading Volume 2 of OpenStax's college Calculus textbook and using our accompanying online resources.
