By Soo T. Tan
Using a transparent, concise writing variety, and use of correct, actual global examples, Soo Tan introduces summary mathematical recommendations together with his intuitive method that brings summary principles to existence. in accordance with this emphasis on conceptual knowing, every one workout set starts with notion questions and every end-of-chapter overview part comprises fill-in-the-blank questions that are helpful for learning the definitions and theorems in each one bankruptcy. also, many questions requesting the translation of graphical, numerical, and algebraic effects are incorporated between either the examples and the workout units.
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Extra resources for Single Variable Calculus (Available 2011 Titles Enhanced Web Assign)
Sample text
Solution To find the length of the arc, we use Equation (4) to obtain s ϭ 3a 7p 7p bϭ 6 2 The area of the sector is obtained by using Equation (5). Thus, Aϭ ϭ 1 7p 1 2 r u ϭ (3)2 a b 2 2 6 21p 4 The Trigonometric Functions Two approaches are generally used to define the six trigonometric functions. We summarize each approach here. 3 The Trigonometric Functions 31 THE TRIGONOMETRIC FUNCTIONS Hypotenuse The Right Triangle Definition For an acute angle u (see Figure 6), Opposite side ¨ Adjacent side FIGURE 6 y P(x, y) 1 sin u ϭ opp hyp cos u ϭ adj hyp csc u ϭ hyp opp sec u ϭ hyp adj tan u ϭ opp adj cot u ϭ adj opp The Unit Circle Definition Let u denote an angle in standard position, and let P(x, y) denote the point where the terminal side of u meets the unit circle.
1 Lines 9 Angles of Inclination DEFINITION Angle of Inclination The angle of inclination of a line L is the smaller angle f (the Greek letter phi) measured in a counterclockwise direction from the direction of the positive x-axis to L (see Figure 14). y y L FIGURE 14 The angle of inclination is measured in a counterclockwise direction from the direction of the positive x-axis. y L L ƒ ƒ 0 x 0 x Note The angle of inclination f satisfies 0° Յ f Ͻ 180° or, in radian measure, 0 Յ f Ͻ p. P2(x2, y2) P1(x1, y1) ƒ ⌬x The relationship between the slope of a line and the angle of inclination of the line can be seen from examining Figure 15.
T(Ϫx) ϭ (Ϫx)4 Ϫ (Ϫx)2 ϩ 1 ϭ x 4 Ϫ x 2 ϩ 1 ϭ t(x), and we see that t is even. c. h(Ϫx) ϭ (Ϫx) Ϫ 2(Ϫx)2 ϭ Ϫx Ϫ 2x 2, which is neither equal to h(x) nor Ϫh(x), and we conclude that h is neither even nor odd. The graphs of the functions f, t, and h are shown in Figure 13. 2 (a) f(x) ϭ x3 Ϫ x 1 2 x Ϫ4 (c) h(x) ϭ x Ϫ 2x2 EXERCISES 3. If t(x) ϭ Ϫx 2 ϩ 2x, find t(Ϫ2) , t( 13) , t(a 2) , t(a ϩ h) , 1 and . 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.