By Jon Rogawski
Read Online or Download Calculus Early Transcendentals for AP PDF
Best calculus books
The current ebook relies on a one semester path on the collage of Craiova. The aim of this textbook is to supply the heritage that's essential to start up paintings on a Ph. D. thesis in utilized Nonlinear research. My objective is to supply for the scholar a huge point of view within the topic, to demonstrate the wealthy number of phenomena encompassed by way of it and to impart a operating wisdom of crucial suggestions of study of the ideas of the equations.
We examine by way of doing. We study arithmetic by way of doing difficulties. This ebook is the 1st quantity of a chain of books of difficulties in mathematical research. it's in general meant for college kids learning the fundamental rules of study. although, given its association, point, and choice of difficulties, it's going to even be an awesome selection for academic or problem-solving seminars, rather these aimed toward the Putnam examination.
- Introduction to The Theory of Functions of a Complex Variable
- Exercises in Integration
- Calculus I with Precalculus, A One-Year Course, 3rd Edition
- Asymptotics for Dissipative Nonlinear Equations
- Bob Miller's Calc for the Clueless: Calc I (Bob Miller's Clueless Series)
Extra resources for Calculus Early Transcendentals for AP
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.