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By James Stewart

This most sensible promoting writer staff explains innovations easily and obviously, with no glossing over tough issues. challenge fixing and mathematical modeling are brought early and strengthened all through, in order that while scholars end the path, they've got a superior origin within the rules of mathematical pondering. This finished, calmly paced booklet presents whole assurance of the functionality inspiration and integrates great graphing calculator fabrics that support scholars improve perception into mathematical principles. The authors' recognition 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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Example text

3. 7 ϩ 10 ϭ 10 ϩ 7 4. 213 ϩ 5 2 ϭ 13 ϩ 5 2 2 28. (a) 6. 21A ϩ B 2 ϭ 2A ϩ 2B 7. 15x ϩ 1 2 3 ϭ 15x ϩ 3 8. 41 10 12 Ͻ 11 13 1 (b) Ϫ Ͻ Ϫ1 2 (b) 8 Յ 9 32. 1 (b) 8 Յ 8 ■ 7 2 State whether each inequality is true or false. 31. (a) Ϫp Ͼ Ϫ3 33–34 9. 2 x13 ϩ y2 ϭ 13 ϩ y22 x 2 5 1 10 Place the correct symbol (Ͻ, Ͼ, or ϭ) in the space. ■ ■ (b) 29. (a) Ϫ6 Ͻ Ϫ10 30. (a) 5. 1x ϩ 2y 2 ϩ 3z ϭ x ϩ 12y ϩ 3z2 2 Ϫ 34 1 1 2 Ϫ 3 27. (a) 3 29–32 ■ 3–10 Write each statement in terms of inequalities. 33. (a) x is positive 10.

For instance, we must have 20 # 23 ϭ 20ϩ3 ϭ 23 But this can happen only if 20 ϭ 1. Likewise, we want to have 54 # 5Ϫ4 ϭ 54ϩ 1Ϫ42 ϭ 54Ϫ4 ϭ 50 ϭ 1 and this will be true if 5Ϫ4 ϭ 1/54. These observations lead to the following definition. 3 Integer Exponents Example 2 23 Zero and Negative Exponents (a) A 47 B 0 ϭ 1 1 1 (b) x Ϫ1 ϭ 1 ϭ x x 1 1 1 (c) 1Ϫ22 Ϫ3 ϭ ϭϪ 3 ϭ Ϫ8 8 1Ϫ22 ■ Familiarity with the following rules is essential for our work with exponents and bases. In the table the bases a and b are real numbers, and the exponents m and n are integers.

A) y is negative (b) z is greater than 1 (c) b is at most 8 5x ϩ 5y ϭ (d) „ is positive and is less than or equal to 17 (e) y is at least 2 units from p 15–20 ■ Use properties of real numbers to write the expression without parentheses. 15. 31x ϩ y2 16. 1a Ϫ b 2 8 19. Ϫ 52 12 x Ϫ 4y2 20. 13a 2 1b ϩ c Ϫ 2d2 17. 412m 2 21–26 ■ 21. (a) 22. (a) 2 3 ϩ Ϫ 2 3 A6 4 15 3 5 Ϫ 3 2B 24. (a) A3 ϩ 14 B A1 Ϫ 45 B 25. (a) 2 2 3 Ϫ 2 3 2 35–38 ■ (b) 1 4 ϩ 1 5 (b) 1 ϩ Ϫ 5 8 (b) A 12 Ϫ 13 B A 12 ϩ 13 B C ϭ {7, 8, 9, 10} 35.

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