Single Variable Calculus: Early Transcendentals, 6th Edition by James Stewart

By James Stewart

Luck on your calculus direction starts off the following! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, exact, and packed with proper, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, 6th version, Stewart conveys not just the application of calculus that can assist you increase technical competence, but additionally promises an appreciation for the intrinsic fantastic thing about the topic. His sufferer examples and integrated studying aids may help you construct your mathematical self assurance and accomplish your objectives within the direction!

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F͑x͒ ෇ 2x ϩ 1 39. G͑x͒ ෇ 41. f ͑x͒ ෇ 42. f ͑x͒ ෇ 43. f ͑x͒ ෇ 44. f ͑x͒ ෇ f ͑a ϩ 1͒, 2 f ͑a͒, f ͑2a͒, f ͑a 2 ͒, [ f ͑a͒] 2, and f ͑a ϩ h͒. 3x ϩ Խ x Խ x ͭ ͭ ͭ 40. 4 Ϫ t2 2Ϫt Խ x t͑x͒ ෇ Խ Խ Խ x2 x ϩ 2 if x Ͻ 0 1 Ϫ x if x ജ 0 3 Ϫ 12 x 2x Ϫ 5 ͭ if x ഛ 2 if x Ͼ 2 x ϩ 2 if x ഛ Ϫ1 x2 if x Ͼ Ϫ1 xϩ9 Ϫ2x Ϫ6 if x Ͻ Ϫ3 if Խ x Խ ഛ 3 if x Ͼ 3 22. A spherical balloon with radius r inches has volume V͑r͒ ෇ 43 ␲ r 3. Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r ϩ 1 inches.

In a certain country, income tax is assessed as follows. There is no tax on income up to $10,000. Any income over $10,000 is taxed at a rate of 10%, up to an income of $20,000. Any income over $20,000 is taxed at 15%. (a) Sketch the graph of the tax rate R as a function of the income I. 0 5 x 65–70 Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. x2 x4 ϩ 1 65. f ͑x͒ ෇ x x2 ϩ 1 66. f ͑x͒ ෇ 67. f ͑x͒ ෇ x xϩ1 68. f ͑x͒ ෇ x x 69.

We consider several cases. 30 |||| CHAPTER 1 FUNCTIONS AND MODELS (i) a ෇ n, where n is a positive integer The graphs of f ͑x͒ ෇ x n for n ෇ 1, 2, 3, 4, and 5 are shown in Figure 11. 1]. y y=x y=≈ y 1 1 0 1 x 0 y=x# y y x 0 1 x 0 y=x% y 1 1 1 y=x$ 1 1 x 0 1 x FIGURE 11 Graphs of ƒ=x n for n=1, 2, 3, 4, 5 The general shape of the graph of f ͑x͒ ෇ x n depends on whether n is even or odd. If n is even, then f ͑x͒ ෇ x n is an even function and its graph is similar to the parabola y ෇ x 2. If n is odd, then f ͑x͒ ෇ x n is an odd function and its graph is similar to that of y ෇ x 3.

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