Calculus: Early Transcendentals by Soo T. Tan

By Soo T. Tan

Taking a clean method whereas keeping vintage presentation, the Tan Calculus sequence makes use of a transparent, concise writing kind, and makes use of appropriate, actual global examples to introduce summary mathematical thoughts with an intuitive method. according to this emphasis on conceptual realizing, every one workout set within the 3 semester Calculus textual content starts off with notion questions and every end-of-chapter assessment part comprises fill-in-the-blank questions that are worthwhile for getting to know the definitions and theorems in each one bankruptcy. also, many questions inquiring for the translation of graphical, numerical, and algebraic effects are incorporated between either the examples and the workout units. The Tan Calculus 3 semester textual content encourages a true global, program dependent, intuitive figuring out of Calculus with no comprising the mathematical rigor that's beneficial in a Calculus textual content.

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T(3) 2t 2 , find f(2), f(x ϩ 1), and f(2x Ϫ 1). 1t Ϫ 1 1x x ϩ1 and f(x ϩ 2h). 2 10. If f(x) ϭ 2x 2 ϩ 1, find and simplify where h 0. 11. If f(x) ϭ x Ϫ x 2, find and simplify where h 0. 12. If f(x) ϭ 1x, find and simplify where h 0. f(a ϩ h) Ϫ f(a) h , In Exercises 15–26, find the domain of the function. 15. f(x) ϭ 7. If 17. t(t) ϭ x ϩ 1 if x Յ 0 f(x) ϭ e 1x if x Ͼ 0 2 3x ϩ 1 x2 tϩ1 2t 2 Ϫ t Ϫ 1 19. f(x) ϭ 29 Ϫ x 2 21. f(x) ϭ 1x Ϫ 2 ϩ 14 Ϫ x find f(Ϫ2), f(0), and f(1). 8. If 22. f(x) ϭ x if x Ͻ Ϫ1 f(x) ϭ • x ϩ 1 1 ϩ 1x ϩ 1 if x Ն Ϫ1 find f(Ϫ2), f(Ϫ1), and f(0).

A plane flying along a straight path loses altitude at the rate of 1000 ft for each 6000 ft covered horizontally. What is the angle of descent of the plane? 76. 22. If the plane gains altitude of 1000 ft over a certain period of time, what will be the horizontal distance covered by the plane over that period? 77. Truss Bridges Simple trusses are common in bridges. The following figure depicts such a truss superimposed on a coordinate system. Find an equation of the line containing the line segments (a) OD, (b) AD, (c) AC, and (d) BC.

THEOREM 2 Two nonvertical lines are parallel if and only if they have the same slope. Note y Suppose that L 1 and L 2 are two nonvertical perpendicular lines with slopes m 1 and m 2 and angles of inclination f1 and f2, respectively. The case in which f1 is acute and f2 is obtuse is shown in Figure 18. Since 90° Ͻ f2 Ͻ 180°, m 2 is negative, so the length of the side BC is Ϫm 2. The two right triangles ᭝ABC and ᭝DAC are similar, and since the ratios of corresponding sides of similar triangles are equal, we have L1 D L2 A ƒ1 ƒ1 1 If two lines are vertical, then they are parallel.

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