By Ross L. Finney, Franklin D. Demana, Bert K. Waits, Daniel Kennedy
The major objective of this 3rd variation is to realign with the alterations within the complex Placement (AP ) calculus syllabus and the hot form of AP examination questions. we have now additionally extra conscientiously aligned examples and routines and up-to-date the information utilized in examples and routines. Cumulative fast Quizzes at the moment are supplied or thrice in each one chapter.
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Yes y 4. 39. y ϭ 2 ln (3 Ϫ x) Ϫ 4 40. y ϭ Ϫ3 log (x ϩ 2) ϩ 1 41. y ϭ log2 (x ϩ 1) 42. y ϭ log3 (x Ϫ 4) Domain: (Ϫ1, ϱ); Range: all reals No y = 1x 100 50 44. f (x) ϭ ᎏᎏ 43. 1Ϫx 45. Self-inverse Prove that the function f is its own inverse. Ϫෆ x 2ෆ, (a) f (x) ϭ ͙1ෆෆ 6. Yes No y = –3x3 x xՆ0 (b) f (x) ϭ 1͞x 46. Radioactive Decay The half-life of a certain radioactive substance is 12 hours. There are 8 grams present initially. y y = int x (a) Express the amount of substance remaining as a function of t/12 time t.
Justify your answer. True. Circle starting at (2, 0) and ending at (2, 0). t Յ 0 (b) x ϭ y2 Ϫ 3; lower half In Exercises 23–28, find a parametrization for the curve. In Exercises 39 and 40, use the parametric curve x ϭ 5t, y ϭ 3 Ϫ 3t, 0 Յ t Յ 1. 23. the line segment with endpoints (Ϫ1, Ϫ3) and (4, 1) See page 36. 39. Multiple Choice Which of the following describes its graph? (or y ϭ Ϫ͙xෆ; ϩ 3 all) 24. the line segment with endpoints (Ϫ1, 3) and (3, Ϫ2) See page 36. (A) circle 25. the lower half of the parabola x Ϫ 1 ϭ y2 (D) line segment 26.
H determines the x-coordinate of the center of the circle. It causes a horizontal shift of the graph. qxd 1/13/06 8:49 AM Page 36 36 Chapter 1 Prerequisites for Calculus (b) Writing to Learn Let h ϭ 0 and k ϭ Ϫ2, Ϫ1, 1, and 2, in turn. Graph using the parameter interval [0, 2p]. Describe the role of k. k determines the y-coordinate of the center of the circle. It y y=2 causes a vertical shift of the graph. (c) Find a parametrization for the circle with radius 5 and center at (2, Ϫ3). x ϭ 5 cos t Ϫ 3, y ϭ 2 sin t ϩ 4, 0 Յ t Յ 2p In Exercises 45 and 46, a parametrization is given for a curve.