By Soo T. Tan
Combining the simplest of conventional insurance with smooth instruments, market-leading Applied Calculus for the Managerial, existence, and Social Sciences: a quick Approach, 8th version, applies math on your international. It grants simply the precise stability of functions, pedagogy, and know-how that can assist you reach the direction. instructing through program, the textual content is choked with real-life examples that encourage and enlighten you. Its intuitive process introduces summary thoughts via examples drawn from universal studies to you can relate. additionally it is perception from execs approximately how they combine math into their day by day operations. various workouts, together with Diagnostic exams, make sure you have an outstanding knowing of textual content thoughts ahead of advancing to the following topic—or examination. an exhilarating array of supplements—Enhanced WebAssign, resolution video clips, own Tutor—equips you with wide studying help that is helping maximize your learn efforts and increase your grade. casting off the apprehension many scholars suppose after they start this path, Applied Calculus for the Managerial, lifestyles, and Social Sciences: a quick Approach, 8th version, makes use of an available presentation of options and techniques that makes it a good source for majors and non-majors alike.
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Sample text
For example, the polynomial equation x 3 Ϫ 3x 2 ϩ 2x ϭ 0 may be rewritten in the form x(x2 Ϫ 3x ϩ 2) ϭ 0 or x(x Ϫ 1)(x Ϫ 2) ϭ 0 Since the product of two real numbers can be equal to zero if and only if one (or both) of the factors is equal to zero, we have xϭ0 xϪ1ϭ0 or xϪ2ϭ0 from which we see that the desired roots are x ϭ 0, 1, and 2. The Quadratic Formula In general, the problem of finding the roots of a polynomial equation is a difficult one. But the roots of a quadratic equation (a polynomial equation of degree 2) are easily found either by factoring or by using the following quadratic formula.
Thus, 0 x 0 Յ 5 means Ϫ5 Յ x Յ 5 (Figure 5a). To obtain an alternative solution, observe that 0 x 0 is the distance from the point x to zero, so the inequality 0 x 0 Յ 5 implies immediately that Ϫ5 Յ x Յ 5. Solution x FIGURE 5 –5 (a) x 5 0 –5 (b) 0 5 Next, the inequality 0 x 0 Ն 5 states that the distance from x to zero is greater than or equal to 5. 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. Solution The inequality 0 2x Ϫ 3 0 Յ 1 is equivalent to the inequalities Ϫ1 Յ 2x Ϫ 3 Յ 1 (see Example 13).
MEETING PROFIT GOALS A manufacturer of a certain commodity has estimated that her profit in thousands of dollars is given by the expression Ϫ6x2 ϩ 30x Ϫ 10 where x (in thousands) is the number of units produced. What production range will enable the manufacturer to realize a profit of at least $14,000 on the commodity? 90. 08 mg/cc. 91. COST OF REMOVING TOXIC POLLUTANTS A city’s main well was recently found to be contaminated with trichloroethylene (a cancer-causing chemical) as a result of an abandoned chemical dump that leached chemicals into the water.