Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 2 ppsx

... Logarithmic Functions 421 CHAPTER 12 Inverse Functions: Can What Is Done Be Undone? 421 12. 1 What Does It Mean for f and g to Be Inverse Functions? 421 12. 2 Finding the Inverse of a Function 429 12. 3 ... Guardino, Sara Anderson, Michael Boezi, Susan Laferriere, and Barbara Atkinson. And thanks to Elka Block and Frank Purcell, for their comments and suggestions...

Ngày tải lên: 05/07/2014, 18:20

... the input 2 the output 7. The value of f at2is7. 2 f → 7 f (2) =7 The expression y = f(x)is shorthand for “y is the output of f corresponding to an input of x” and it is read “y equals f of x.” When ... A, B, and C, corresponding to machines A, B, and C, respectively. Assign button #1 the number 1, button #2 the number 2, etc. We’ll use the first letter (small case)...

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... (fg)(x), and  f g  (x), and find their domains. 39. f(x)=ax + b and g(x) = cx + d 40. f(x)=3x + 2and g(x) = 5x − 1 41. f(x)=2x + 3and g(x) =x 2 −1 42. f(x)= 3 x+1 and g(x) = 2x x−5 43. f(x)= √ x and ... ,so A=f(r)=f(g(t))=f( √ t) =π( √ t) 2 =πt. t 0 123 45678910 r 0.00 1.00 1.41 1.73 2. 00 2. 23 2. 44 2. 65 2. 83 3.00 3.16 A 0.00 3.14 6 .28 9. 42 12. 57 15.71 18.85...

Ngày tải lên: 05/07/2014, 18:20

... of items sold in the week. A(x) = 25 0 + 10x and B(x) = 20 0 + 20 x Graphs of A(x) and B(x) are drawn below. x A B $ 325 300 27 5 25 0 22 5 20 0 123 456 Figure 4.13 We are most likely interested in an ... position to be a function of time, quantity demanded to be a function of price, and velocity to be a function of time. i. Suppose s is position, in miles,...

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... =−x 2 is an example of a parabola opening downward. x = y 2 is an example of a parabola opening to the right, and x =−y 2 is an example of a parabola opening to the left. y x y = –x 2 x = –y 2 y x x ... 0. 14. Solve: (x − 2) 4 − 2( x − 2) 2 =−1. 6 .2 Quadratics From A Noncalculus Perspective 22 5 other terms and determines the sign and behavior of f ....

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... can get a handle on this limit by dividing the numerator and denominator by the highest power of x occurring in the denominator: lim x→∞ x 2 − 1 2x 2 − x − 3 = lim x→∞ x 2 x 2 − 1 x 2 2x 2 x 2 − x x 2 − 3 x 2 = ... graphing calculator. Your answers to parts (a) and (b) ought to agree with your answer to part (c). You can use your answers to parts (a) and (b...

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... that x and y are related by x 2 + y 2 = 25 . Relating the variables x and y allows us to relate their rates of change. Because x and y vary with time, we can write [x(t)] 2 +[y(t)] 2 =25 . (a) ... increasing? 2. The price and the demand for a certain item can be modeled by the equation 20 p =−q +20 0. (a) Express the rate of change of quantity demanded with resp...

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... signs. x 2 –π 2 π π 2 3π 2 –3π 2 –π 2 tan x Figure 19 .20 Between x = 0 and x = π /2, the numerator and denominator are positive. The numerator is increasing and the denominator is approaching ... 1 2 10 1 2 1 2 1 2 y y x y yy y x xx x x (i) (iii) (iv) (v) (vi) (ii) –1 2 1 2 1 2 1 2 10 20 60 –1 2 1 2 1 –1 2 1 2 1 2 14. The region of Bogor in Java...

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... the triangle we see that sin(π/3) = √ 3 2 cos(π/3) = 1 2 tan(π/3) = √ 3 sin(π/6) = 1 2 cos(π/6) = √ 3 2 tan(π/6) = 1 √ 3 π 3 π 3 π 6 2 1 1 1 √3 2 1 2 1 2 1 2 1 2 √3 2 √3 2 √3 v uu v π 3 2 1 2 1 ( ( , P( ) ... “angle of elevation” and “angle of depression.” Angle of elevation refers to the angle from the horizontal up to an object; angle of depressio...

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... (b) −π 2 (c) 2 − π 2 = 3π 2 EXERCISE 22 .2 Suppose that f is continuous on the interval [−1, 3]. We partition [−1, 3] into n equal subintervals, each of length x, and form left- and right-hand ... 1 and t = 3. 22 .2 The Definite Integral 725 (b) the distance traveled between t = 0 and t = 8. (c) the distance traveled between t = 3 and t = 5. v(t) t 12 2 34 4 56 6 78...

Ngày tải lên: 05/07/2014, 18:20