A First Course in Calculus, 3rd Edition by Serge Lang

By Serge Lang

This 5th variation of Lang's ebook covers all of the issues normally taught within the first-year calculus series. Divided into 5 elements, every one portion of a primary direction IN CALCULUS includes examples and purposes in relation to the subject coated. additionally, the rear of the e-book includes precise strategies to various the routines, letting them be used as worked-out examples -- one of many major advancements over earlier variations.

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Y ϭ x 3 Ϫ x In Exercises 5–14, sketch the graph of the equation by point plotting. 1 5. y ϭ 2 x ϩ 2 6. y ϭ 5 Ϫ 2x 7. y ϭ 4 Ϫ x 2 8. y ϭ ͑x Ϫ 3͒2 9. y ϭ Խx ϩ 2Խ 10. y ϭ Խ x Խ Ϫ 1 12. y ϭ Ίx ϩ 2 11. y ϭ Ίx Ϫ 6 13. y ϭ 3 x 14. y ϭ 1 xϩ2 In Exercises 15 and 16, describe the viewing window that yields the figure. 15. y ϭ x3 ϩ 4x 2 Ϫ3 21. y ϭ x 2 ϩ x Ϫ 2 22. y 2 ϭ x3 Ϫ 4x 23. y ϭ xΊ16 Ϫ 24. y ϭ ͑x Ϫ 1͒Ίx2 ϩ 1 x2 2 Ϫ Ίx 5x 27. x 2y Ϫ x 2 ϩ 4y ϭ 0 x 2 ϩ 3x ͑3x ϩ 1͒2 28. y ϭ 2x Ϫ Ίx 2 ϩ 1 26. y ϭ In Exercises 29– 40, test for symmetry with respect to each axis and to the origin.

Subtract 1 from each side. Zeros of g ■ NOTE Each of the functions in Example 5 is either even or odd. However, some functions, such as f ͑x͒ ϭ x 2 ϩ x ϩ 1, are neither even nor odd. com for worked-out solutions to odd-numbered exercises. 3 x 2 xϪ1 In Exercises 1 and 2, use the graphs of f and g to answer the following. 19. f ͑x͒ ϭ (a) Identify the domains and ranges of f and g. In Exercises 21–26, find the domain of the function. (b) Identify f ͧ؊2ͨ and gͧ3ͨ. (d) Estimate the solution(s) of f ͧxͨ ‫ ؍‬2.

Y y y 4 m1 = 4 1 5 3 4 m2 = 0 y (0, 4) m3 = −5 3 3 (− 1, 2) 4 (3, 4) 3 2 2 m4 is undefined. 1 1 (3, 1) (2, 2) 2 (3, 1) (−2, 0) −2 −1 1 1 x −1 1 2 3 If m is positive, then the line rises from left to right. 13 −2 −1 x −1 1 2 3 If m is zero, then the line is horizontal. x −1 2 −1 (1, − 1) 3 4 If m is negative, then the line falls from left to right. x −1 1 2 4 −1 If m is undefined, then the line is vertical. 2 EXPLORATION Investigating Equations of Lines Use a graphing utility to graph each of the linear equations.

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