By James Stewart

This top promoting writer staff explains ideas easily and obviously, with no glossing over tricky issues. challenge fixing and mathematical modeling are brought early and bolstered all through, in order that while scholars end the path, they've got an effective starting place within the ideas of mathematical considering. This finished, flippantly paced publication offers entire assurance of the functionality suggestion and integrates colossal graphing calculator fabrics that support scholars advance perception into mathematical principles. The authors' realization to aspect and readability, as in James Stewart's market-leading Calculus textual content, is what makes this article the industry chief.

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**Extra resources for Algebra and trigonometry, 2nd Edition **

**Example text**

So we can always find a number in the interval 10, 1 2 closer to zero than any given number. Since 0 itself is not in the interval, the interval contains no smallest number. 9999 closer yet, and so on. Since 1 itself is not in the interval, the interval has no largest number. Example 6 Finding Unions and Intersections of Intervals Graph each set. (a) 11, 32 പ 32, 74 (b) 11, 32 ʜ 32, 74 Solution (a) The intersection of two intervals consists of the numbers that are in both intervals. Therefore 11, 32 പ 32, 74 ϭ 5x 0 1 Ͻ x Ͻ 3 and 2 Յ x Յ 76 ϭ 5x 0 2 Յ x Ͻ 36 ϭ 32, 32 This set is illustrated in Figure 7.

4 5 3 2 x x 3 3 2 3 3 ͙ 5 ළ#͙ 5 ළ ϭ͙ 5 ළ ϭ5 ͙ළළ x3 Multiply by ᎏᎏ ᎑ 5 3 ͙ ළළ x 5 5 2 # 5 3 5 ͙ xළළ ͙xළළ ϭ ͙xළළ5 ϭ x Radical expression Exponential expression 1 15 1. 3 19–22 ■ Evaluate the expression using x ϭ 3, y ϭ 4, and z ϭ Ϫ1. 19. 2x 2 ϩ y 2 21. 19x2 2/3 ϩ 12y2 2/3 ϩ z 2/3 23–32 27 2. 2 42/3 3. ■ 5 3 2 5 5. 6. 5 7. a 2/5 24. 175 ϩ 148 25. 1125 Ϫ 145 3 3 26. 1 54 Ϫ 1 16 2x 5 ■ Evaluate each expression. 9. (a) 116 10. (a) 164 11. (a) 13. (a) A 49 B Ϫ1/2 14. (a) 1024 15. (a) A 321 B 2/5 16. 5 18.

5 Ͻ x Ͻ 2 72. 135 53–54 ■ Express each set in interval notation. Applications 53. (a) (b) −3 0 5 −3 0 5 54. (a) 0 (b) −2 73. Area of a Garden Mary’s backyard vegetable garden measures 20 ft by 30 ft, so its area is 20 ϫ 30 ϭ 600 ft 2. She decides to make it longer, as shown in the figure, so that the area increases to A ϭ 20130 ϩ x 2 . Which property of real numbers tells us that the new area can also be written A ϭ 600 ϩ 20x? 2 Apago PDF Enhancer 0 30 ft ■ 55. 1Ϫ2, 02 ʜ 1Ϫ1, 1 2 56. 1Ϫ2, 0 2 പ 1Ϫ1, 1 2 57.