By Ross L. Finney, Franklin D. Demana, Bert K. Waits, Daniel Kennedy
The major objective of this 3rd version is to realign with the adjustments within the complex Placement (AP ) calculus syllabus and the recent form of AP examination questions. now we have additionally extra rigorously aligned examples and workouts and up to date the knowledge utilized in examples and workouts. Cumulative quickly Quizzes at the moment are supplied or 3 times in every one chapter.
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Extra info for Calculus: Graphical, Numerical, Algebraic
Standardized Test Questions You should solve the following problems without using a graphing calculator. 52. True or False The function displayed in the graph below is one-to-one. Justify your answer. False. It fails the horizontal line test. There are horizontal y lines that intersect the curve 3 times. For example, the x-axis. Extending the Ideas 59. One-to-One Functions If ƒ is a one-to-one function, prove that g(x) ϭ Ϫf (x) is also one-to-one. 60. One-to-One Functions If ƒ is a one-to-one function and f (x) is never zero, prove that g(x) ϭ 1͞f (x) is also one-to-one.
Explain what you see, and describe the role of a and b in these parametric equations. ) [–6, 6] by [–8, 8] In Exercises 33 and 34, find a parametrization for the part of the graph that lies in Quadrant I. Possible answer: x ϭ t, y ϭ ͙tෆ, ϩ3 tϾ0 33. y ϭ x 2 ϩ 2x ϩ 2 Possible answer: x ϭ t, y ϭ t2 34. y ϭ ͙ෆ xϩ3 ϩ 2t ϩ 2, t > 0 35. Circles Find parametrizations to model the motion of a particle that starts at (a, 0) and traces the circle x 2 ϩ y 2 ϭ a2, a Ͼ 0, as indicated. See page 36. (a) once clockwise (b) once counterclockwise (c) twice clockwise (d) twice counterclockwise 36.
Y y = int x (a) Express the amount of substance remaining as a function of t/12 time t. Amount ϭ 8 ᎏ1ᎏ 2 (b) When will there be 1 gram remaining? 1 x y Domain: (4, ϱ); Range: all reals In Exercises 43 and 44, find a formula for f Ϫ1 and verify that ( f ؠf Ϫ1)(x) ϭ ( f Ϫ1 ؠƒ)(x) ϭ x. f Ϫ1(x) ϭ log y = 21 x +1 x 5. 05 34. 97 33. 045)t ϭ 2 Yes 47. 75% compounded annually. 936 years. ) In Exercises 7–12, determine whether the function has an inverse function. 3 7. y ϭ ᎏᎏ Ϫ 1 Yes 8. y ϭ x 2 ϩ 5x No 9.