By James Stewart

James Stewart's well-received CALCULUS: options AND CONTEXTS, moment version follows within the course of the opposite best-selling books by way of this striking writer. the 1st version of this publication was once hugely winning since it reconciled faculties of inspiration: it skillfully merged the simplest of conventional calculus with the simplest of the reform circulation. This re-creation keeps to provide the balanced procedure besides Stewart's hallmark gains: meticulous accuracy, sufferer motives, and punctiliously graded difficulties. The content material has been subtle and the examples and routines were up to date. furthermore, CALCULUS: strategies AND CONTEXTS, moment version now contains a loose CD-ROM for college kids that comprises animations, actions, and homework tricks. The booklet integrates using the CD all through by utilizing icons that express scholars whilst to exploit the CD to deepen their knowing of a tough notion. In CALCULUS: options AND CONTEXTS, this good revered writer emphasizes conceptual realizing - motivating scholars with genuine international purposes and stressing the guideline of 4 in numerical, visible, algebraic, and verbal interpretations. All innovations are awarded within the vintage Stewart type: with simplicity, personality, and a focus to aspect. as well as his transparent exposition, Stewart additionally creates good thought-out difficulties and workouts. The definitions are unique and the issues create an amazing stability among conceptual knowing and algebraic talents.

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**Extra resources for Calculus: Concepts and Contexts (2nd Edition)**

**Example text**

FIGURE 13 The f • g machine is composed of the g machine (first) and then the f machine. x (input) g g(x) f f{ ©} (output) f•g f g FIGURE 14 Arrow diagram for f • g x © f{ ©} EXAMPLE 7 If f ͑x͒ x 2 and t͑x͒ x Ϫ 3, find the composite functions f ؠt and t ؠf . SOLUTION We have ͑ f ؠt͒͑x͒ f ͑t͑x͒͒ f ͑x Ϫ 3͒ ͑x Ϫ 3͒2 ͑t ؠf ͒͑x͒ t͑ f ͑x͒͒ t͑x 2 ͒ x 2 Ϫ 3 | You can see from Example 7 that, in general, f ؠt t ؠf . Remember, the notation f ؠt means that the function t is applied first and then f is applied second.

13. (a) Temperature (°F) Chirping rate (chirps͞min) 50 55 60 65 70 75 80 85 90 20 46 79 91 113 140 173 198 211 (b) y y 0 x 0 14. (a) (b) y y 37 x (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Use the linear model in part (b) to estimate the chirping rate at 100 ЊF. 17. The table gives the winning heights for the Olympic pole vault competitions in the 20th century. 0 ■ ■ x ■ ■ ■ ■ 0 ■ ■ x ■ ■ ■ ■ ■ 15. The table shows (lifetime) peptic ulcer rates (per 100 popu- lation) for various family incomes as reported by the 1989 National Health Interview Survey.

_3 % 0 6 3 x _3 4. The graph of f is given. Draw the graphs of the following functions. 3 NEW FUNCTIONS FROM OLD FUNCTIONS 13. y cos͑x͞2͒ 5. The graph of f is given. Use it to graph the following functions. (a) y f ͑2x͒ (c) y f ͑Ϫx͒ 14. y x 2 ϩ 2x ϩ 3 15. y 1 xϪ3 16. y Ϫ2 sin x y 17. y 1 sin x Ϫ 3 6 18. y 2 ϩ 1 19. y 1 ϩ 2x Ϫ x 2 20. y 2 sx ϩ 4 Ϫ 3 21. y 2 Ϫ sx ϩ 1 22. y ͑x Ϫ 1͒3 ϩ 2 (b) y f ( 12 x) (d) y Ϫf ͑Ϫx͒ 0 x 1 ͩ ͪ Խ 23. y sin x 6–7 ■ The graph of y s3x Ϫ x is given.