By Saturnino L. Salas; Garret J. Etgen; Einar Hille;
For ten variations, readers have became to Salas to profit the tough recommendations of calculus with out sacrificing rigor. The booklet regularly presents transparent calculus content material to assist them grasp those thoughts and comprehend its relevance to the true global. through the pages, it deals an ideal stability of concept and functions to raise their mathematical insights. Readers also will locate that the publication emphasizes either problem-solving talents and real-world purposes.
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Extra info for Calculus: One and Several Variables, 10th Edition
13. 15. 17. 19. x − 1 < 0. x 2 − x − 6 ≥ 0. 2x 2 + x − 1 ≤ 0. x(x − 1)(x − 2) > 0. x 3 − 2x 2 + x ≥ 0. x 3 (x − 2)(x + 3)2 < 0. x 2 (x − 2)(x + 6) > 0. 2 8. 10. 12. 14. 16. 18. 20. x 2 + 9x + 20 < 0. x 2 − 4x − 5 > 0. 3x 2 + 4x − 4 ≥ 0. x(2x − 1)(3x − 5) ≤ 0. x 2 − 4x + 4 ≤ 0. x 2 (x − 3)(x + 4)2 > 0. 7x(x − 4)2 < 0. Exercises 21–36. Solve the inequality and express the solution set as an interval or as the union of intervals. 21. |x| < 2. 22. |x| ≥ 1. 23. |x| > 3. 24. |x − 1| < 1. 26. |x − 12 | < 2.
68. Express the volume of a cube as a function of one of the diagonals. 69. Express the area of an equilateral triangle as a function of the length of a side. 70. A right triangle with hypotenuse c is revolved about one of its legs to form a cone. ) Given that x is the length of the other leg, express the volume of the cone as a function of x. 15:42 P1: PBU/OVY P2: PBU/OVY JWDD023-01 JWDD023-Salas-v13 QC: PBU/OVY T1: PBU October 5, 2006 32 ■ CHAPTER 1 PRECALCULUS REVIEW y (2, 5) c (x, 0) x 71. A Norman window is a window in the shape of a rectangle surmounted by a semicircle.
Theorem (a phony one): 1 = 2. 3 REVIEW OF INEQUALITIES x −2<4 ■ (the inequality has been reversed) 15:42 P1: PBU/OVY P2: PBU/OVY JWDD023-01 JWDD023-Salas-v13 QC: PBU/OVY T1: PBU October 5, 2006 12 ■ CHAPTER 1 PRECALCULUS REVIEW To isolate x, we multiply by −1. This gives x ≤ 8. (the inequality has been reversed again) ❏ The solution set is the interval (−∞, 8]. 8 There are generally several ways to solve a given inequality. For example, the last inequality could have been solved as follows: −3(4 − x) ≤ 12, −12 + 3x ≤ 12, 3x ≤ 24, (we added 12) x ≤ 8.