Calculus Early Transcendentals by James Stewart

By James Stewart

Good fortune on your calculus direction starts off right here! James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are world-wide best-sellers for a cause: they're transparent, actual, and jam-packed with proper, real-world examples. With CALCULUS: EARLY TRANSCENDENTALS, 8th version, Stewart conveys not just the software of calculus that will help you enhance technical competence, but in addition grants an appreciation for the intrinsic great thing about the topic. His sufferer examples and integrated studying aids may help you construct your mathematical self assurance and attain your objectives within the path.

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Example text

F ͑a ϩ 1͒, 2 f ͑a͒, f ͑2a͒, f ͑a 2 ͒, [ f ͑a͒] 2, and f ͑a ϩ h͒. 26. A spherical balloon with radius r inches has volume V͑r͒ ෇ 43 ␲ r 3. Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r ϩ 1 inches. 27–30 Evaluate the difference quotient for the given function. Simplify your answer. 38. Find the domain and range and sketch the graph of the 39–50 Find the domain and sketch the graph of the function. 39. 4x 40. F ͑x͒ ෇ x 2 Ϫ 2x ϩ 1 41.

Y y y _2 (_2, 0) FIGURE 14 0 (a) x=¥-2 x _2 0 (b) y=œ„„„„ x+2 x 0 (c) y=_ œ„„„„ x+2 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. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

The most useful representation of the area of a circle as a function of its radius is probably the algebraic formula A͑r͒ ෇ ␲ r 2, though it is possible to compile a table of values or to sketch a graph (half a parabola). Because a circle has to have a positive radius, the domain is ͕r r Ͼ 0͖ ෇ ͑0, ϱ͒, and the range is also ͑0, ϱ͒. Խ t Population (millions) 0 10 20 30 40 50 60 70 80 90 100 110 1650 1750 1860 2070 2300 2560 3040 3710 4450 5280 6080 6870 B. We are given a description of the function in words: P͑t͒ is the human population of the world at time t.