By Soo T. Tan

Within the market-leading CALCULUS FOR THE MANAGERIAL, lifestyles, AND SOCIAL SCIENCES, Soo T. Tan offers a correct, obtainable presentation of calculus mixed with simply the fitting stability of purposes, pedagogy, and know-how to aid scholars achieve the direction. the hot 7th variation comprises hugely fascinating present purposes and routines to aid stimulate scholar motivation. a thrilling new array of vitamins, together with iLrn educational and the Interactive Video Skillbuilder CD-ROM, presents scholars with huge studying help so teachers could have extra time to target instructing the center ideas.

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**Extra resources for Calculus for the Managerial, Life, and Social Sciences, Seventh Edition**

**Sample text**

This line can be constructed as follows. Arbitrarily select a point on a straight line to represent the number 0. This point is called the origin. If the line is horizontal, then a point at a convenient distance to the right of the origin is chosen to represent the number 1. This determines the scale for the number line. Each positive real number lies at an appropriate distance to the right of the origin, and each negative real number lies at an appropriate distance to the left of the origin (Figure 1).

2 xϪ1 x(x Ϫ 1)(2x ϩ 1) (x Ϫ 1)2(2x2 ϩ 1)1Ϫ1/2 x(4x3 Ϫ 6x2 ϩ x Ϫ 2) ϭ ᎏᎏᎏ (x Ϫ 1)2(2x2 ϩ 1)1/2 12x2 12x2 ෆϭᎏ 2x2 ϩ 3 ᎏ ϩ 6(2x2 ϩ 3)1/2 b. ᎏᎏ ϩ 6œෆ (2x2 ϩ 3)1/2 ෆ 2x2 ϩ 3 œෆ 12x2 ϩ 6(2x2 ϩ 3)1/2(2x2 ϩ 3)1/2 ϭ ᎏᎏᎏᎏ (2x2 ϩ 3)1/2 Write radicals in exponential form. LCD is (2x 2 ϩ 3)1/2. 12x2 ϩ 6(2x2 ϩ 3) ᎏ ϭᎏ (2x2 ϩ 3)1/2 6(4x2 ϩ 3) 24x2 ϩ 18 ϭᎏ ᎏ ϭ ᎏ ᎏ (2x2 ϩ 3)1/2 2x2 ϩ ෆ3 œෆ Rationalizing Algebraic Fractions When the denominator of an algebraic fraction contains sums or differences involving radicals, we may rationalize the denominator—that is, transform the fraction into an equivalent one with a denominator that does not contain radicals.

Like terms may be combined by adding or subtracting their numerical coefficients. For example, 3x ϩ 7x ϭ 10x and 1 7 ᎏᎏxy ϩ 3xy ϭ ᎏᎏxy 2 2 The distributive property of the real number system, ab ϩ ac ϭ a(b ϩ c) is used to justify this procedure. To add or subtract two or more algebraic expressions, first remove the parentheses and then combine like terms. The resulting expression is written in order of decreasing degree from left to right. * EXAMPLE 1 a. (2x4 ϩ 3x3 ϩ 4x ϩ 6) Ϫ (3x4 ϩ 9x3 ϩ 3x2) ϭ 2x4 ϩ 3x3 ϩ 4x ϩ 6 Ϫ 3x4 Ϫ 9x3 Ϫ 3x2 ϭ 2x4 Ϫ 3x4 ϩ 3x3 Ϫ 9x3 Ϫ 3x2 ϩ 4x ϩ 6 ϭ Ϫx4 Ϫ 6x3 Ϫ 3x2 ϩ 4x ϩ 6 Remove parentheses.