Calculus Early Transcendentals by James Stewart

By James Stewart

Luck on your calculus direction begins right here! James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are world-wide best-sellers for a cause: they're transparent, exact, and jam-packed with appropriate, real-world examples. With CALCULUS: EARLY TRANSCENDENTALS, 8th variation, Stewart conveys not just the software of calculus that will help you improve technical competence, but additionally grants an appreciation for the intrinsic fantastic thing about the topic. His sufferer examples and integrated studying aids may help you construct your mathematical self assurance and accomplish your pursuits within the direction.

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May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 97909_00_ch00_p001-008:97909_00_ch00_p001-008 6 10/8/10 11:12 AM Page 6 A PREVIEW OF CALCULUS The concept of the limit of a sequence occurs whenever we use the decimal representation of a real number.

For instance, the sequence {1, 12 , 13 , 14 , 15 , . } can be described by giving the following formula for the nth term: an ෇ a¢ a£ a™ 0 1 n We can visualize this sequence by plotting its terms on a number line as in Figure 10(a) or by drawing its graph as in Figure 10(b). Observe from either picture that the terms of the sequence a n ෇ 1͞n are becoming closer and closer to 0 as n increases. In fact, we can find terms as small as we please by making n large enough. We say that the limit of the sequence is 0, and we indicate this by writing a¡ 1 (a) 1 lim nlϱ 1 2 3 4 5 6 7 8 1 ෇0 n n In general, the notation (b) FIGURE 10 lim a n ෇ L nlϱ is used if the terms a n approach the number L as n becomes large.

A) f ͑x͒ ෇ sx ϩ 2 (b) t͑x͒ ෇ 1 x Ϫx 2 SOLUTION (a) Because the square root of a negative number is not defined (as a real number), the domain of f consists of all values of x such that x ϩ 2 ജ 0. This is equivalent to x ജ Ϫ2, so the domain is the interval ͓Ϫ2, ϱ͒. Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.

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