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Chapter 10: An Introduction to Calculus: Limits, Derivatives, and Integrals
We have made some significant changes to this chapter from previous editions of the book. Our goal is to //set the stage// for the study of calculus by looking at two classical problems of motion. Through the tools of analytic geometry (which should be well-honed by the end of this course), we show that one problem leads geometrically to the slopes of tangent lines, while the other leads geometrically to areas under curves. We show how both problems can be solved using limits (intuitively defined), and we sprinkle the whole chapter liberally with perspectives from history. In short, we hope that this chapter will give you an appreciation for the "calculus step" that you will make next year. We want to set the stage for you without spoiling the first act.