Transcription of Limit of a Function
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Limit of a Function
Limit of a FunctionChapter 2In This ChapterMany topics are included in a typical course in calculus. But the three most fun-damental topics in this study are the concepts of Limit , derivative, and integral. Each of these con-cepts deals with functions, which is why we began this text by first reviewing some importantfacts about functions and their , two problems are used to introduce the basic tenets of calculus. These are thetangent line problemand the area problem. We will see in this and the subsequent chapters thatthe solutions to both problems involve the Limit An Informal That Involve A Formal Tangent Line ProblemChapter 2 in Reviewy (x)Lax a xy (x) L (x) Lx a 9/26/09 5:20 PM Page 67 Jones and Bartlett Publishers, LLC.
The number 1Lis said to be the left-hand limit of as x approaches a. Similarly, if can be made arbitrarily close to a number L 2 by taking xsufficiently close to, but not equal to, a num- ber a from the right, then L 2 is the right-hand limit of as approaches x a and we write (4) The quantities in (3) and (4) are also referred to as one-sided limits. Two-Sided LimitsIf both the left-hand ...
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