By Soo T. Tan
Within the market-leading CALCULUS FOR THE MANAGERIAL, existence, AND SOCIAL SCIENCES, Soo T. Tan presents a correct, available presentation of calculus mixed with simply the suitable stability of functions, pedagogy, and know-how to assist scholars achieve the direction. the recent 7th version contains hugely attention-grabbing present purposes and workouts to assist stimulate scholar motivation. a thrilling new array of supplementations, together with iLrn educational and the Interactive Video Skillbuilder CD-ROM, offers scholars with huge studying aid so teachers could have extra time to target instructing the center thoughts.
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Extra resources for Calculus for the managerial, life, and social sciences, (7th Edition)
Your calculator will give the answer 3 when you use it to evaluate œ9 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, equivaq p b whenever it exists. 8283 and 1 1 1 1 ᎏ ϭ ᎏ1/2 ᎏ ϭ ᎏᎏ5 ϭ ᎏᎏ 4Ϫ5/2 ϭ ᎏ5/2 4 (4 )5 2 32 The rules defining the exponential expression an, where a Ͼ 0 for all rational values of n, are given in Table 3. 1 PRECALCULUS REVIEW I 7 TABLE 3 Rules for Defining an Definition of an (a a 0) Definition of an (a a 0) Example Fractional exponent: a.
6 @ Ϫ27y e x Ϫ1/2 82. ᎏxϪ ᎏ e 2@ xϪ3 2 y 4 83. ᎏᎏ@ y x (r n)4 84. ᎏ ᎏ r 5Ϫ2n 85. œ3 ෆ xϪ2 и œෆ 4x5 86. œෆ 81x6yϪ4ෆ 87. Ϫœ4 ෆ 16x4y8 88. œ3 ෆ x3aϩb 89. œ6 ෆ 64 x8y 3 90. œ3 ෆ 27r 6 и œෆ s2t 4 114. CELSIUS AND FAHRENHEIT TEMPERATURES The relationship between Celsius (°C) and Fahrenheit (°F) temperatures is given by the formula 5 C ϭ ᎏᎏ (F Ϫ 32) 9 a. If the temperature range for Montreal during the month of January is Ϫ15° Ͻ °C Ͻ Ϫ5°, find the range in degrees Fahrenheit in Montreal for the same period.
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. 2 PRECALCULUS REVIEW II 21 This procedure is illustrated in Example 12. 1 EXAMPLE 12 Rationalize the denominator: ᎏᎏ. 1 ϩ œxෆ Solution Upon multiplying the numerator and the denominator by (1 Ϫ œxෆ), we obtain 1 1 1 Ϫ œxෆ ᎏᎏ ϭ ᎏᎏ и ᎏᎏ 1 ϩ œxෆ 1 ϩ œxෆ 1 Ϫ œxෆ 1 Ϫ ͙xෆ ᎏᎏ ϭ 1 1 Ϫ ͙xෆ 1 Ϫ œxෆ ϭ ᎏᎏ2 1 Ϫ (œxෆ) 1 Ϫ œxෆ ϭ ᎏᎏ 1Ϫx In other situations, it may be necessary to rationalize the numerator of an algebraic expression.