# Algebra and Trigonometry by Sheldon Axler

By Sheldon Axler

Collage Algebra and Trigonometry will entice those that are looking to supply vital issues extra in-depth, higher-level insurance. this article deals streamlined process followed with obtainable definitions throughout all chapters to permit for an easy-to-understand learn. university Algebra comprises prose that's designated, exact, and simple to learn, with hassle-free definitions of even the themes which are ordinarily so much tricky for readers.

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Extra resources for Algebra and Trigonometry

Example text

For example, (19 − 12 − 8) − 2 = −3. 2 Algebra of the Real Numbers 21 Thus ten values are possible; they are −418, −382, −238, −3, 1, 13, 17, 23, 113, and 139. 3. 6 + 3 · 4 + 5 · 2 solution Here are the possibilities: (6 + 3 · 4 + 5 · 2) = 28 6 + (3 · 4 + 5) · 2 = 40 (6 + 3) · 4 + 5 · 2 = 46 6 + 3 · (4 + 5 · 2) = 48 6 + 3 · (4 + 5) · 2 = 60 Other possible ways to insert one pair of parentheses lead to values already included in the list above. For example, solution (x + y + z)2 = (x + y + z)(x + y + z) = x(x + y + z) + y(x + y + z) + z(x + y + z) = x 2 + xy + xz + yx + y 2 + yz + zx + zy + z2 = x 2 + y 2 + z2 + 2xy + 2xz + 2yz 13.

Give four examples of pairs of real numbers a and b such that |a + b| = 2 and |a| + |b| = 8. 34. Give four examples of pairs of real numbers a and b such that |a + b| = 3 and |a| + |b| = 11. 34 chapter 1 The Real Numbers In Exercises 35–46, write each set as an interval or as a union of two intervals. 35. {x : |x − 4| < 36. {x : |x + 2| < 1 } 10 1 } 100 ε }; here 2 37. ] 38. {x : |x − 2| < 3ε }; here ε > 0 44. {x : |x| > 9} 45. {x : |x − 5| ≥ 3} 46. {x : |x + 6| ≥ 2} The intersection of two sets of numbers consists of all numbers that are in both sets.

9 should mean. 09. Make sure you know how your calculator interprets the kind of input shown in the example above, or you may get answers from your calculator that do not reflect the problem you have in mind. 2 Algebra of the Real Numbers 17 Many calculators have parentheses buttons, which are often needed to control the order in which operations are performed. 3101. Calculators and computers have evolved from being able to do arithmetic to having serious symbolic and graphing abilities. For now, we will focus on the ability of symbolic calculators to perform algebraic simplifications.