By Soo T. Tan
Within the market-leading CALCULUS FOR THE MANAGERIAL, lifestyles, AND SOCIAL SCIENCES, Soo T. Tan offers a correct, available presentation of calculus mixed with simply the fitting stability of purposes, pedagogy, and expertise to assist scholars reach the direction. the recent 7th variation comprises hugely attention-grabbing present functions and workouts to assist stimulate scholar motivation. a thrilling new array of supplementations, together with iLrn instructional and the Interactive Video Skillbuilder CD-ROM, offers scholars with broad studying help so teachers could have extra time to target instructing the center ideas.
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This booklet is an English translation of the final French version of Bourbaki’s Fonctions d'une Variable Réelle.
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Additional info for Calculus for the Managerial, Life, and Social Sciences, Seventh Edition
EXAMPLE 2 Let P(x, y) denote a point lying on the circle with radius r and center C(h, k) (Figure 8). Find a relationship between x and y. Solution By the definition of a circle, the distance between C(h, k) and P(x, y) is r. Using Formula (1), we have y P(x, y) ෆ Ϫ hෆ )2 ϩ (yෆ Ϫ k)2 ϭ r œ(x r which, upon squaring both sides, gives the equation C(h, k) (x Ϫ h)2 ϩ (y Ϫ k)2 ϭ r 2 x FIGURE 8 A circle with radius r and center C(h, k) that must be satisfied by the variables x and y. A summary of the result obtained in Example 2 follows.
P Ϫ 1͉ ϩ 2 Έ Έ Ϫ8 ᎏ Ίᎏ 27 3 165/8161/2 55. ᎏᎏ 167/8 9Ϫ3 и 95 Ϫ1/2 56. ᎏϪᎏ 9 2 @ 57. 9 58. 4 In Exercises 59–68, determine whether the statement is true or false. Give a reason for your choice. 59. x4 ϩ 2x4 ϭ 3x4 60. 32 и 22 ϭ 62 ෆ ͉Ϫ2͉ 26. ͉Ϫ1͉ ϩ œ2 61. x3 и 2x2 ϭ 2x6 62. 33 ϩ 3 ϭ 34 28. ͉p Ϫ 6͉ Ϫ 3 24x 63. ᎏ3ᎏx ϭ 24xϪ3x 1 64. (22 и 32)2 ϭ 64 1 1 65. ᎏϪ3 ᎏ ϭ ᎏᎏ 4 64 43/2 1 66. ᎏᎏ ϭ ᎏᎏ 24 2 67. 21/2)Ϫ1/2 ϭ 1 68. 52/3 и (25)2/3 ϭ 25 ෆ Ϫ 1͉ ϩ ͉3 Ϫ œ2 ෆ͉ 29. ͉œ2 ෆ Ϫ 3͉ Ϫ ͉œ3 ෆ Ϫ 4͉ 30. ͉2œ3 In Exercises 31–36, suppose a and b are real numbers other than zero and that a a b.
B 3. C 4. D 5. E 6. F In Exercises 7–12, refer to the following figure. y y D B 3 A 2 B C 1 x –5 –3 –1 4 1 3 5 7 –6 A D –4 x –2 9 2 4 –2 F 6 G E –3 –5 C F –4 7. Which point has coordinates (4, 2)? 8. What are the coordinates of point B? E –7 9. Which points have negative y-coordinates? 3 10. Which point has a negative x-coordinate and a negative y-coordinate? 11. Which point has an x-coordinate that is equal to zero? 12. Which point has a y-coordinate that is equal to zero? In Exercises 13–20, sketch a set of coordinate axes and plot each point.