By Maurice D. Weir, George B. Thomas Jr., Joel R. Hass

This textual content is designed for the one variable portion of a three-semester or four-quarter calculus direction (math, engineering, and technological know-how majors).

Calculus hasn’t replaced, yet your scholars have. Today’s scholars were raised on immediacy and the will for relevance, they usually come to calculus with diverse mathematical backgrounds. Thomas’ Calculus: Early Transcendentals, 12th Edition, is helping your scholars effectively generalize and practice the main principles of calculus via transparent and specific causes, fresh layout, thoughtfully selected examples, and improved workout units. Thomas bargains the correct mix of simple, conceptual, and difficult routines, besides significant functions. this crucial revision beneficial properties extra examples, extra mid-level routines, extra figures, and more advantageous conceptual flow.

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Additional info for Thomas' Calculus Early Transcendentals (12th Edition)

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Cos ax + 2p b - 2 3 Graph the functions in Exercises 23–26 in the ts-plane (t-axis horizontal, s-axis vertical). What is the period of each function? What symmetries do the graphs have? 23. s = cot 2t 24. s = - tan pt 25. s = sec a t 26. s = csc a b 2 pt b 2 Solving Trigonometric Equations For Exercises 51–54, solve for the angle u, where 0 … u … 2p. 3 51. sin2 u = 52. sin2 u = cos2 u 4 53. sin 2u - cos u = 0 Theory and Examples 55. The tangent sum formula The standard formula for the tangent of the sum of two angles is T 27.

Y = sx + 1d2>3 42. y = sx - 8d2>3 43. y = 1 - x 2>3 44. y + 4 = x 2>3 45. y = 2x - 1 - 1 3 3>2 46. y = sx + 2d + 1 1 sx - 1d2 52. y = a. g s -td b. -g std c. g std + 3 d. 1 - g std e. g s - t + 2d f. g st - 2d g. g s1 - td h. -g st - 4d 57. y = x 2 - 1, 58. y = x - 1, compressed horizontally by a factor of 2 1 59. y = 1 + 2 , x compressed vertically by a factor of 2 1 , stretched horizontally by a factor of 3 x2 61. y = 2x + 1, compressed horizontally by a factor of 4 1 - 1 x2 1 1 + 1 54. y = x2 sx + 1d2 55.

055 times its value in the previous year. 46 In general, the amount after x years is given by P(1 + r) x, where r is the interest rate (expressed as a decimal). qxd 10/1/09 2:24 PM Page 36 36 Chapter 1: Functions For integer and rational exponents, the value of an exponential function ƒ(x) = a x is obtained arithmetically as follows. If x = n is a positive integer, the number a n is given by multiplying a by itself n times: y y ϭ 10 x a n = 1442443 a # a # Á # a. 5 1 (a) y ϭ 2 x, y ϭ 3 x, y ϭ 10 x If x = 1>n for some positive integer n, then x n a 1>n = 2a, which is the positive number that when multiplied by itself n times gives a.

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