By Earl W. Swokowski, Jeffery A. Cole
Transparent motives, an uncluttered and beautiful format, and examples and routines that includes numerous real-life functions have made this article renowned between scholars yr after yr. This most up-to-date variation of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY keeps those gains. the issues were always praised for being at simply the precise point for precalculus scholars such as you. The booklet additionally offers calculator examples, together with particular keystrokes that assist you to use quite a few graphing calculators to unravel difficulties extra quick. probably such a lot important-this publication successfully prepares you for extra classes in arithmetic.
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Extra info for Algebra and Trigonometry with Analytic Geometry
N (2) If a Ͼ 0, then 2a is the positive real number b such that bn ϭ a. n (3) (a) If a Ͻ 0 and n is odd, then 2a is the negative real number b such n that b ϭ a. n (b) If a Ͻ 0 and n is even, then 2a is not a real number. 4, are needed to define 2a if a Ͻ 0 and n is an even positive integer, because for all real numbers b, bn Ն 0 whenever n is even. 2 If n ϭ 2, we write 2a instead of 2 a and call 2a the principal square 3 root of a or, simply, the square root of a. The number 2 a is the (principal) cube root of a.
2 Exponents and Radicals 21 We usually use 5(a) if m Ͼ n and 5(b) if m Ͻ n. We can extend laws of exponents to obtain rules such as ͑abc͒n ϭ anbncn and amanap ϭ amϩnϩp. Some other examples of the laws of exponents are given in the next illustration. ILLUS TRATION Laws of Exponents x5x6x2 ϭ x5ϩ6ϩ2 ϭ x13 ͑ y 5͒7 ϭ y 5и7 ϭ y 35 ͑3st͒4 ϭ 34s4t 4 ϭ 81s4t 4 ͩͪ c8 ϭ c8Ϫ3 ϭ c5 c3 u3 1 1 ϭ 8Ϫ3 ϭ 5 8 u u u p 2 5 ϭ p5 p5 ϭ 25 32 To simplify an expression involving powers of real numbers means to change it to an expression in which each real number appears only once and all exponents are positive.
Note the difference between a negative real number and the negative of a real number. In particular, the negative of a real number a can be positive. For example, if a is negative, say a ϭ Ϫ3, then the negative of a is Ϫa ϭ Ϫ͑Ϫ3͒ ϭ 3, which is positive. In general, we have the following relationships. Relationships Between a and ؊a (1) If a is positive, then Ϫa is negative. (2) If a is negative, then Ϫa is positive. In the following chart we define the notions of greater than and less than for real numbers a and b.