By Earl W. Swokowski, Jeffery A. Cole
Transparent factors, an uncluttered and attractive format, and examples and workouts that includes various real-life functions have made this article well known between scholars 12 months after 12 months. This most modern version of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY keeps those positive factors. the issues were continually praised for being at simply the proper point for precalculus scholars such as you. The publication additionally offers calculator examples, together with particular keystrokes that assist you use a variety of graphing calculators to resolve difficulties extra fast. possibly such a lot important-this ebook successfully prepares you for extra classes in arithmetic.
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Extra resources for Algebra and Trigonometry with Analytic Geometry
B Laws of Signs (1) If a and b have the same sign, then ab and The converses* of the laws of signs are also true. For example, if a quotient is negative, then the numerator and denominator have opposite signs. The notation a Ն b, read “a is greater than or equal to b,” means that either a Ͼ b or a ϭ b (but not both). For example, a2 Ն 0 for every real number a. The symbol a Յ b, which is read “a is less than or equal to b,” means that either a Ͻ b or a ϭ b. Expressions of the form a Ն b and a Յ b are called nonstrict inequalities, since a may be equal to b.
A polynomial in x is a sum of any number of monomials in x. Another way of stating this is as follows. Copyright 2008 Thomson Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 3 Algebraic Expressions Definition of Polynomial 33 A polynomial in x is a sum of the form an x n ϩ anϪ1x nϪ1 ϩ и и и ϩ a1 x ϩ a0, where n is a nonnegative integer and each coefficient ak is a real number. If an 0, then the polynomial is said to have degree n. Each expression ak x k in the sum is a term of the polynomial.
Definition of Rational Exponents Let m͞n be a rational number, where n is a positive integer greater than 1. n If a is a real number such that 2 a exists, then n (1) a1/n ϭ 2 a m n n m m/n (2) a ϭ ͑ 2 a ͒ ϭ 2 a m/n 1/n m m 1/n (3) a ϭ ͑a ͒ ϭ ͑a ͒ n When evaluating am/n in (2), we usually use ͑ 2 a ͒ ; that is, we take the nth root of a first and then raise that result to the mth power, as shown in the following illustration. m The Exponential Notation a m/n ILLUS TRATION 5 5 3 x3/5 ϭ ͑ 2 x͒ ϭ 2 x 3 x1/3 ϭ 2 x 3 3 3 3 2 1252/3 ϭ ͑2 125 ͒2 ϭ ͑2 5 ͒ ϭ 52 ϭ 25 32 3/5 32 3 ͑243 ͒ ϭ ͙͑5 243 ͒ ϭ ͙͑5 ͑23 ͒5͒3 ϭ ͑23 ͒3 ϭ 278 TI-83/4 Plus Rational Exponents ٙ 8 Ϫ8 ٙ ( 5 ( 32 TI-86 Ϭ 1 ( Ϭ 1 243 Ϭ 3 ) ) MATH ) 3 ) ٙ Ϫ8 ENTER ( ٙ 8 ENTER 3 Ϭ 1 ENTER ٙ ( 5 ( 32 Ϭ 1 ( Ϭ 1 243 ) 3 Ϭ ) 3 ) ENTER ٙ ENTER ( 3 Ϭ ) 2nd MORE MATH Frac(F1) MISC(F5) ENTER The Frac command changes a decimal representation to a fractional representation.
Algebra and Trigonometry with Analytic Geometry by Earl W. Swokowski, Jeffery A. Cole