By Jon Rogawski

Rogawski's outstanding textbook was once instantly acclaimed for balancing formal precision with a guiding conceptual concentration that engages scholars whereas reinforcing the relevance of calculus to their lives and destiny studies.  specific formal proofs, brilliant examples, colourful pix, intuitive factors, and striking challenge units all interact for an creation to the direction that's enticing and enduring.  Watch teacher video studies here.

Now Rogawski's Calculus returns in a meticulously up to date re-creation, in a model designed in particular for AP courses.  Rogawski's Calculus for AP*, moment Edition includes a new coauthor, Ray Cannon, previously AP Calculus leader Reader for the school Board.  between different contributions, Dr. Cannon wrote this version's end-of-chapter a number of selection and loose reaction Questions, giving scholars the chance to paintings a similar form of difficulties they're going to see at the AP exam.

TEACHERS: obtain now Rogawski's Calculus for AP*, moment variation Early Transcendentals, that includes bankruptcy three, Differentiation

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Extra resources for Calculus Early Transcendentals for AP

Sample text

Y 70. Extend the graph of f (x) to [−4, 4] so that it is an odd function. y y = x2 4 3 3 2 −4 1 0 x y = f (x) FIGURE 29 x 1 2 3 FIGURE 27 4 71. Suppose that f (x) has domain [4, 8] and range [2, 6]. Find the domain and range of: (a) f (x) + 3 (b) f (x + 3) (c) f (3x) (d) 3f (x) 72. Let f (x) = x 2 . Sketch the graph over [−2, 2] of: (a) f (x + 1) (b) f (x) + 1 (c) f (5x) (d) 5f (x) 73. Suppose that the graph of f (x) = sin x is compressed horizontally by a factor of 2 and then shifted 5 units to the right.

1 s 1 t In Exercises 49–52, determine where f (x) is increasing. 49. f (x) = |x + 1| 50. f (x) = x 3 51. f (x) = x 4 1 52. f (x) = 4 x + x2 + 1 In Exercises 53–58, find the zeros of f (x) and sketch its graph by plotting points. Use symmetry and increase/decrease information where appropriate. 53. f (x) = x 2 − 4 54. f (x) = 2x 2 − 4 55. f (x) = x 3 − 4x 56. f (x) = x 3 57. f (x) = 2 − x 3 58. f (x) = 1 (x − 1)2 + 1 59. Which of the curves in Figure 26 is the graph of a function? y y x 34. Represent 1/7 and 4/27 as repeating decimals.

If the temperature is changed by an amount T , then the rod’s length changes by L = αL0 T , where α is the thermal expansion coefficient. 24 × 10−5 ◦ C−1 . (a) A steel rod has length L0 = 40 cm at T0 = 40◦ C. Find its length at T = 90◦ C. (b) Find its length at T = 50◦ C if its length at T0 = 100◦ C is 65 cm. (c) Express length L as a function of T if L0 = 65 cm at T0 = 100◦ C. 28. 2), (2, 2) lie on a line? 29. Find b such that (2, −1), (3, 2), and (b, 5) lie on a line. 30. Find an expression for the velocity v as a linear function of t that matches the following data.