By Soo T. Tan
Popular for accuracy, Soo Tan's utilized CALCULUS FOR THE MANAGERIAL, existence, AND SOCIAL SCIENCES, 8th variation balances purposes, pedagogy, and know-how to supply scholars the context they should remain stimulated within the path and attracted to the cloth. available for majors and non-majors alike, the textual content makes use of an intuitive process that introduces summary innovations via examples drawn from universal, real-life stories to which scholars can relate. It additionally attracts functions from readers' fields of curiosity. furthermore, insightful Portfolios spotlight the careers of genuine humans and talk about how they comprise math into their day-by-day operations. quite a few exercises--including new Diagnostic Tests--ensure scholars have a superb figuring out of thoughts earlier than advancing to the following subject. Algebra evaluate notes, keyed to the assessment bankruptcy Preliminaries, seem the place scholars want them, once they desire them. Bringing robust assets to students' fingertips, the text's fascinating array of vitamins, together with stronger net Assign, equips scholars with huge studying help to aid them maximize their research time.
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Extra info for Applied Calculus for the Managerial, Life, and Social Sciences (8th Edition)
96. | a Ϫ b | ϭ | b Ϫ a | 97. | a Ϫ b | Յ | b | ϩ | a | 98. 1, we saw how a one-to-one correspondence between the set of real numbers and the points on a straight line leads to a coordinate system on a line (a onedimensional space). A similar representation for points in a plane (a two-dimensional space) is realized through the Cartesian coordinate system, which is constructed as follows: Take two perpendicular lines, one of which is normally chosen to be horizontal. These lines intersect at a point O, called the origin (Figure 7).
Next, recall that if p /q (p, q, positive integers with q 0) is a rational number in lowest terms, then the expression b p/q is defined as the number (b1/q) p or, equivalently, q 2b p, whenever it exists. 8283 Expressions involving negative rational exponents are taken care of by the definition b Ϫp/q ϭ 1 b p/q Thus, 4Ϫ5/2 ϭ 1 1 1 1 ϭ 1/2 5 ϭ 5 ϭ 5/2 2 32 4 14 2 The rules defining the exponential expression an, where a Ͼ 0 for all rational values of n, are given in Table 3. The first three definitions in Table 3 are also valid for negative values of a.
2x ϩ y)(2x Ϫ y) 92. (3x ϩ 2)(2 Ϫ 3x) 93. (x2 Ϫ 1)(2x) Ϫ x2(2x) 94. 1x 1/2 1 1 ϩ 1 2¢ x Ϫ1/2≤ Ϫ 1x1/2 Ϫ 1 2¢ x Ϫ1/2≤ 2 2 123. 4(x Ϫ 1)2(2x ϩ 2)3(2) ϩ (2x ϩ 2)4(2)(x Ϫ 1) 124. (x2 ϩ 1)(4x3 Ϫ 3x2 ϩ 2x) Ϫ (x4 Ϫ x3 ϩ x2)(2x) 125. (x2 ϩ 2)2[5(x2 ϩ 2)2 Ϫ 3](2x) 126. (x2 Ϫ 4)(x2 ϩ 4)(2x ϩ 8) Ϫ (x2 ϩ 8x Ϫ 4)(4x3) 95. 21t ϩ 1t2 2 Ϫ 2t 2 In Exercises 127–132, find the real roots of each equation by factoring. 96. 2x2 ϩ (Ϫx ϩ 1)2 127. x2 ϩ x Ϫ 12 ϭ 0 128. 3x2 Ϫ x Ϫ 4 ϭ 0 129. 4t 2 ϩ 2t Ϫ 2 ϭ 0 130. Ϫ6x2 ϩ x ϩ 12 ϭ 0 In Exercises 97–104, factor out the greatest common factor from each expression.
Applied Calculus for the Managerial, Life, and Social Sciences (8th Edition) by Soo T. Tan