By Soo T. Tan
Popular for accuracy, Soo Tan's utilized CALCULUS FOR THE MANAGERIAL, lifestyles, AND SOCIAL SCIENCES, 8th variation balances purposes, pedagogy, and expertise to supply scholars the context they should remain stimulated within the direction and attracted to the cloth. available for majors and non-majors alike, the textual content makes use of an intuitive technique that introduces summary innovations via examples drawn from universal, real-life stories to which scholars can relate. It additionally attracts purposes from readers' fields of curiosity. furthermore, insightful Portfolios spotlight the careers of genuine humans and speak about how they comprise math into their day-by-day operations. a number of exercises--including new Diagnostic Tests--ensure scholars have a great realizing of innovations earlier than advancing to the following subject. Algebra evaluation notes, keyed to the assessment bankruptcy Preliminaries, look the place scholars want them, once they want them. Bringing strong assets to students' fingertips, the text's fascinating array of vitamins, together with stronger internet Assign, equips scholars with large studying help to aid them maximize their learn time.
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Additional info for Applied Calculus for the Managerial, Life, and Social Sciences (8th Edition)
This observation yields the result x Ն 5 or x Յ Ϫ5 (Figure 5b). EXAMPLE 14 Solve the inequality 0 2x Ϫ 3 0 Յ 1. The inequality 0 2x Ϫ 3 0 Յ 1 is equivalent to the inequalities Ϫ1 Յ 2x Ϫ 3 Յ 1 (see Example 13). Thus, 2 Յ 2x Յ 4 and 1 Յ x Յ 2. The solution is therefore given by the set of all x in the interval [1, 2] (Figure 6). 2 Exercises In Exercises 1–6, simplify the expression. x ϩxϪ2 x2 Ϫ 4 2 1. 2a Ϫ 3ab Ϫ 9b 2ab2 ϩ 3b3 2 2. 12t 2 ϩ 12t ϩ 3 3. ᎏ 4t 2 Ϫ 1 2 x3 ϩ 2x2 Ϫ 3x 4. Ϫ2x2 Ϫ x ϩ 3 5. 14x Ϫ 1 2 13 2 Ϫ 13x ϩ 1 2 14 2 6.
If a Ͻ b and c Ͻ 0, then ac Ͼ bc. 2 Ͻ 3 and 3 Ͻ 8, so 2 Ͻ 8. Ϫ5 Ͻ Ϫ3, so Ϫ5 ϩ 2 Ͻ Ϫ3 ϩ 2; that is, Ϫ3 Ͻ Ϫ1. Ϫ5 Ͻ Ϫ3, and since 2 Ͼ 0, we have (Ϫ5)(2) Ͻ (Ϫ3)(2); that is, Ϫ10 Ͻ Ϫ6. Ϫ2 Ͻ 4, and since Ϫ3 Ͻ 0, we have (Ϫ2)(Ϫ3) Ͼ (4)(Ϫ3); that is, 6 Ͼ Ϫ12. Similar properties hold if each inequality sign, Ͻ, between a and b and between b and c is replaced by Ն, Ͼ, or Յ. Note that Property 4 says that an inequality sign is reversed if the inequality is multiplied by a negative number. A real number is a solution of an inequality involving a variable if a true statement is obtained when the variable is replaced by that number.
Using the quadratic formula, we find Ϫ5 Ϯ 252 Ϫ 412 2 1Ϫ12 2 Ϫb Ϯ 2b 2 Ϫ 4ac ϭ 2a 212 2 Ϫ5 Ϯ 1121 Ϫ5 Ϯ 11 ϭ ϭ 4 4 3 ϭ Ϫ4 or 2 xϭ This equation can also be solved by factoring. Thus, 2x 2 ϩ 5x Ϫ 12 ϭ (2x Ϫ 3)(x ϩ 4) ϭ 0 from which we see that the desired roots are x ϭ 32 or x ϭ Ϫ4, as obtained earlier. *In this book, we are interested only in the real roots of an equation. 1 PRECALCULUS REVIEW I 13 b. We first rewrite the given equation in the standard form x 2 ϩ 3x Ϫ 8 ϭ 0, from which we see that a ϭ 1, b ϭ 3, and c ϭ Ϫ8.