Download Algebra and Trigonometry with Analytic Geometry, Classic by Earl Swokowski, Jeffery A. Cole PDF

By Earl Swokowski, Jeffery A. Cole

The most recent version within the hugely revered Swokowski/Cole precalculus sequence keeps the weather that experience made it so well liked by teachers and scholars alike: its exposition is obvious, the time-tested workout units function various functions, its uncluttered format is beautiful, and the trouble point of difficulties is acceptable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage version, 12E, successfully prepares scholars for additional classes in arithmetic via its first-class, time-tested challenge units

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3 If 2a ϭ b, then b2 ϭ a; that is, ͑ 2a͒2 ϭ a. If 2 a ϭ b, then b3 ϭ a, or 3 3 ͑ 2 a ͒ ϭ a. Generalizing this pattern gives us property 1 in the next chart. n Properties of 2a (n is a positive integer) Property (1) (2) (3) (4) ͑ 2n a ͒n ϭ a if 2n a is a real number n 2 an ϭ a if a Ն 0 n 2 a ϭ a if a Ͻ 0 and n is odd n n 2 an ϭ ͉ a ͉ if a Ͻ 0 and n is even Illustrations ͑ 25͒2 ϭ 5, ͑ 23 Ϫ8 ͒3 ϭ Ϫ8 2͑Ϫ2͒ ϭ Ϫ2, 2 ͑Ϫ2͒5 ϭ Ϫ2 2͑Ϫ3͒2 ϭ ͉ Ϫ3 ͉ ϭ 3, 2 ͑Ϫ2͒4 ϭ ͉ Ϫ2 ͉ ϭ 2 2 52 ϭ 5, 3 3 3 3 2 2 ϭ2 5 4 If a Ն 0, then property 4 reduces to property 2.

EXAMPLE 6 Rationalizing a denominator Rationalize the denominator: 1 2x ϩ 2y SOLUTION 1 1 2x Ϫ 2y multiply numerator and denominator by ϭ и 2x ϩ 2y 2x ϩ 2y 2x Ϫ 2y the conjugate of 2x ϩ 2y 2x Ϫ 2y property of quotients and difference of ϭ squares ͑ 2x ͒2 Ϫ ͑ 2y ͒2 2x Ϫ 2y law of radicals ϭ xϪy L In calculus it is sometimes necessary to rationalize the numerator of a quotient, as shown in the following example. EXAMPLE 7 If h Rationalizing a numerator 0, rationalize the numerator of 2x ϩ h Ϫ 2x .

4 3 x 47 2 3 5 x 48 2 3 ͑a ϩ b͒2 49 2 50 ͙a ϩ 2b 51 2x ϩ y 3 3 r Ϫ s3 52 2 2 2 26 CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA Exer. 53–56: Rewrite the expression using a radical. 53 (a) 4x (b) ͑4x͒ 3/2 3/2 3/2 54 (a) 4 ϩ x (b) ͑4 ϩ x͒3/2 55 (a) 8 Ϫ y1/3 (b) ͑8 Ϫ y͒1/3 56 (a) 8y1/3 (b) ͑8y͒1/3 Exer. 57 – 80: Simplify the expression, and rationalize the denominator when appropriate. 57 281 3 Ϫ125 58 2 5 Ϫ64 59 2 4 256 60 2 61 1 62 3 22 ͱ 1 7 63 29xϪ4y6 64 216a8bϪ2 3 8a6bϪ3 65 2 4 81r 5s 8 66 2 67 69 71 73 ͱ ͱ ͱ ͱ 3x 2y3 68 3 2x 4y4 9x 70 4 5x 8y3 27x 2 72 5x7y2 8x 3 74 5 4 ͑3x 5yϪ2͒4 75 2 77 ͱ ͱ 5 8x 3 y4 5 4x 4 y2 3 3 3t 4v 2 2 Ϫ9tϪ1v 4 79 2 ͱ ͱ ͱ ͱ 1 3x 3y 3 3x 2y 5 4x 4 x 7y12 125x 5 3x11y3 9x 2 6 ͑2uϪ3v4͒6 76 2 78 25xy7 210x 3y 3 3 ͑2r Ϫ s͒3 80 2 Exer.

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