By William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Drawing on their many years of training adventure, William Briggs and Lyle Cochran have created a calculus textual content that incorporates the teacher’s voice past the study room. That voice—evident within the narrative, the figures, and the questions interspersed within the narrative—is a grasp instructor best readers to deeper degrees of figuring out. The authors attract readers’ geometric instinct to introduce primary suggestions and lay the root for the extra rigorous improvement that follows. finished workout units have got compliment for his or her creativity, caliber, and scope. This e-book is an improved model of Calculus: Early Transcendentals through an analogous authors, with a complete bankruptcy dedicated to differential equations, extra sections on different themes, and extra routines in so much sections.
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Extra resources for Calculus for Scientists and Engineers: Early Transcendentals
F 1x2 = 3x 4 - 10; 14. g1y2 = 41. f ؠg 42. g ؠf 43. f ؠG 44. f ؠg ؠG 45. G ؠg ؠf 46. F ؠg ؠg 3- 4, 44 * 3- 4, 44 47. g ؠg 48. G ؠG 3- 3, 24 * 30, 24 49–54. Missing piece Let g1x2 = x 2 + 3. Find a function f that produces the given composition. y + 1 ; 1y + 221y - 32 15. f 1x2 = 24 - x 2; 4 16. F 1w2 = 22 - w; 3 17. h1u2 = 2 u - 1; 3- 4, 64 * 3- 3, 34 3- 7, 94 * 3- 2, 24 18. g1x2 = 1x 2 - 421x + 5; 19. f 1x2 = 19 - x 223>2; 20. g1t2 = 1 ; 1 + t2 41–48. More composite functions Let f 1x2 = ͉x͉, g1x2 = x 2 - 4, F 1x2 = 1x, and G1x2 = 1>1x - 22.
For x 7 2, the slope of the line is - 12 and it passes through 14, 32, so an equation of this piece of the function is 1 1 2 3 x 4 1 1 y - 3 = - 1x - 42 or y = - x + 5. 21 For x = 2, we have g122 = 3. Therefore, g1x2 = d (2, 1) 1 x 1 yϭ x 3 if x 6 2 if x = 2 1 - x + 5 if x 7 2. 2 Related Exercises 19–22 x2 Ϫ 5x ϩ 6 if x ϶ 2 xϪ2 if x ϭ 2 1 EXAMPLE 4 ➤ y Graphing piecewise functions Graph the following functions. x 2 - 5x + 6 if x ϶ 2 a. f 1x2 = c x - 2 1 if x = 2 b. 22 y SOLUTION a. The function f is simplified by factoring and then canceling x - 2, assuming x ϶ 2: y ϭ ͉x͉ 1x - 221x - 32 x 2 - 5x + 6 = = x - 3.
What is an appropriate domain for d? 3 y ϭ g(x) 2 1 Additional Exercises 0 95–101. Combining even and odd functions Let E be an even function and O be an odd function. Determine the symmetry, if any, of the following functions. 95. E + O 96. E # O 97. E>O 99. E ؠE 100. O ؠO 101. O ؠE 98. E ؠO 1 2 3 4 5 6 7 8 9 x QUICK CHECK ANSWERS 1. 3, x 4 - 2x 2, t 2 - 2t, p 2 - 4p + 3 2. Domain is all real numbers; range is 5 y: 0 6 y … 1 6. 3. 1 f ؠg21x2 = x 4 + 1 and 1g ؠf 21x2 = 1x 2 + 122.