Calculus: Early Transcendentals (6th Edition) (Stewart's by James Stewart

By James Stewart

Luck on your calculus direction starts off the following! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, exact, and jam-packed with suitable, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, 6th version, Stewart conveys not just the software of calculus that will help you strengthen technical competence, but additionally offers an appreciation for the intrinsic great thing about the topic. His sufferer examples and integrated studying aids might help you construct your mathematical self assurance and accomplish your targets within the path!

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4 2 32. Find the domain and range and sketch the graph of the function h͑x͒ ෇ s4 Ϫ x 2 . 33– 44 Find the domain and sketch the graph of the function. 19. The number N (in millions) of cellular phone subscribers worldwide is shown in the table. ) t 1990 1992 1994 1996 1998 2000 N 11 26 60 160 340 650 (a) Use the data to sketch a rough graph of N as a function of t. (b) Use your graph to estimate the number of cell-phone subscribers at midyear in 1995 and 1999. 20. Temperature readings T (in °F) were recorded every two hours from midnight to 2:00 PM in Dallas on June 2, 2001.

Y 1 0 FIGURE 17 x 1 SOLUTION The line through ͑0, 0͒ and ͑1, 1͒ has slope m ෇ 1 and y-intercept b ෇ 0, so its equation is y ෇ x. Thus, for the part of the graph of f that joins ͑0, 0͒ to ͑1, 1͒, we have f ͑x͒ ෇ x N Point-slope form of the equation of a line: The line through ͑1, 1͒ and ͑2, 0͒ has slope m ෇ Ϫ1, so its point-slope form is y Ϫ 0 ෇ ͑Ϫ1͒͑x Ϫ 2͒ y Ϫ y1 ෇ m͑x Ϫ x 1 ͒ See Appendix B. if 0 ഛ x ഛ 1 So we have f ͑x͒ ෇ 2 Ϫ x or y෇2Ϫx if 1 Ͻ x ഛ 2 We also see that the graph of f coincides with the x-axis for x Ͼ 2.

M In the following example we start with a verbal description of a function in a physical situation and obtain an explicit algebraic formula. The ability to do this is a useful skill in solving calculus problems that ask for the maximum or minimum values of quantities. A rectangular storage container with an open top has a volume of 10 m3. The length of its base is twice its width. Material for the base costs $10 per square meter; material for the sides costs $6 per square meter. Express the cost of materials as a function of the width of the base.

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