Business Calc Homework w answers_Part_6

Business Calc Homework w answers_Part_6 - 26 Section 1.5 x2...

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Unformatted text preview: 26 Section 1.5 x2 y 1, x 1 16. y 2 x ,x y 1 For x 0 (f 0 2 (the domain of f ), 1 f )(x) x 1 1 20. y x )(x) f( x 1) f )(x) 1 f (x (x x 2 x ,x 17. y ), (x 2)2 1 1 2 f 1 1 1 or x 1/2 x For x 1 x 1 )(x) (f f x f( x 1)2 2 x Interchange x and y. For x 1 (f 1/2 x or x f )(x) f 1 )(x) (f f For x f( f )(x) 1 f ), x)2 ( (x 2) (x 2/3)3/2, x y 3/2 x2 x x 0 1 f x 3/2 1 0 (the domain of f 1 )(x) for x f (x 3/2 ) f )(x) 1 (x 3/2 2/3 f 2/3 (x ) 2)2, x 2)2 y, x ) x 2 (x ) x 1 x 0 y or 1 x1/2 )(x) f ), 1 (1/ x)2 x 0 (the domain of f ), f )(x) 1 x3 1 y 31 y f 1 11 x2 x2 1/x 2 1 3 y 1 y 2 1 1 Interchange x and y. ( x)1/2 x or 2 f Verify. 3 1 x (x) 1 3 or x 1 x1/3 Verify. For x (f f (f x x (x) x x3 y 2 1 1 0 (the domain of f 1 22. y Interchange x and y. f 1) 1 1 1 For x 2/3 3/2 y 2 y 1 x 2 x 1 0 1 (x) (f f 2 x 1 For x ), 0, (the domain of f ), (x (x 2x Verify. For x 19. y 1 1) 1)2 1 x Verify. (f 2 x (x) 1 x 1 y y (f f 2 Interchange x and y. Interchange x and y. f 1 ,x x2 1 ,x y 1 y 21. y x x x 2x 2 x 0 y 3/2 3/2 (x 2 (x x x2 x 2/3, x 18. y x) 1 (x 0, (the domain of f ), 1 (f 1 0 (the domain of f x 1 (the domain of f ), 1 x Verify. For x 1] ), 2( 2 x)2 x 1 1) x [( 0 (x) 1) 1 0 (the domain of f x) f x 1 y (x) ( 1 x x ( y 2) 1 y x (x 1 1 2 Verify. 1) 2 1) , x x 2 1), x 2 (x x x 1) 2 x Interchange x and y. 0, (the domain of f ), 1 (f 1) 2x y 2 (x 2 y 1) x ( (x y 1 1 (the domain of f 1 For x 1)1/2 1 or (x Verify. For x (f f 2)2) 2 y (x) ( (x 2 x Interchange x and y. f 1 f 1 0 (the domain of f 1 )(x) f (2 (f f x) x) [(2 ( ) 2 x) 2]2 x (f x 1 1 1 1 3 (1/ x)3 1 )(x) f f )(x) x 1 f13 x 3 3 1/x3 x x x x Section 1.5 2x x 23. y 1 3 x x 24. y xy 3y 2x 2x 1 2)x 1 3y x 1 y 2y x 3 xy 3y (y xy 1 xy x 2y 3 x(y 1 x f 1 1 x 2x x y f 3x 2 1 )(x) f 2 1 x 1 3x x2 1 3x x2 5x 5 1 f )(x) f 3 1 3 2x x 1 3 1 5x 5 2) 2) (f 1 f )(x) x 3 1 3 1 1 3 x x x x Graph of f 3(x 2(x 1) 1) x 3 2 3 2 3 2 3 1 3) 3) 3(x 2) (x 2) x et t : x2 Graph of y 3) 3) t, y1 25. Graph of f: x1 1 2 x 2(x (x 5x 5 2 3 1x f 2 1) 3) 3 1 (2x (2x 5x 5 3 (x 3) 3(2x (2x 1) 2(x 2x x f 1 3 x 2x x )(x) 2x x 2x x x 1 2x 1 1 3x 2 2(1 3x) (x (1 3x) 3(x (f 2x x Verify. (f f 1 3 3 1 (x) Verify. (f f 2y 3 1 Interchange x and y. 3x 2 (x) 1) 2y y x 3y 2 Interchange x and y. y 3 2 e , y2 t t, y3 x: x3 t [ 6, 6] by [ 4, 4] 26. Graph of f: x1 Graph of f Graph of y 1 t, y1 : x2 x: x3 [ 6, 6] by [ 4, 4] 3t 3t, y2 t, y3 t t 27 28 Section 1.5 27. Graph of f: x1 Graph of f 1 t, y1 : x2 Graph of y t 2 33. t 2 , y2 t t, y3 t x: x3 [ 10, 5] by [ 7, 3] Domain: ( , 3) Range: ( , ) 34. [ 4.5, 4.5] by [ 3, 3] 28. Graph of f: x1 Graph of f 1 t, y1 3 t, y2 : x2 Graph of y t 3 t t, y3 t x: x3 [ 5, 10] by [ 5, 5] Domain: ( 2, ) Range: ( , ) 35. [ 4.5, 4.5] by [ 3, 3] 29. Graph of f: x1 Graph of f 1 t, y1 : x2 Graph of y ln t ln t, y2 t t, y3 t x: x3 [ 3, 6] by [ 2, 4] Domain: ( 1, ) Range: ( , ) 36. [ 4.5, 4.5] by [ 3, 3] 30. Graph of f: x1 Graph of f 1 t, y1 : x2 Graph of y log t [ 2, 10] by [ 2, 4] log t, y2 t, y3 x: x3 t Domain: (4, ) Range: ( , ) t 37. (1.045)t 2 t ln(1.045) ln 2 t ln 1.045 ln 2 t [ 4.5, 4.5] by [ 3, 3] 31. Graph of f: x1 Graph of f 1 Graph of y sin sin 1 1 t t, y2 t, y3 x: x3 15.75 Graphical support: t, y1 : x2 ln 2 ln 1.045 t t [ 2, 18] by [ 1, 3] 38. e 0.05t ln e 0.05t [ 3, 3] by [ 2, 2] 32. Graph of f: x1 Graph of f Graph of y 1 0.05t t, y1 : x2 x: x3 tan 1 1 t, y2 t, y3 t t ln 3 0.05 3 ln 3 ln 3 20 ln 3 t tan t Graphical support: [ 5, 35] by [ 1, 4] [ 6, 6] by [ 4, 4] 21.97 Section 1.5 39. e x e x e x 3 3 x e e x(e x 3 (e x)2 3e x x ex 0 x e e x(0) ) 1 3 1 1 2 0 ( 3)2 2(1) 5 3 e 43. y 100 2 2 3 ln 100 y x 100 y x log2 x 5 x 0.96 or 0.96 2 1 100 1 y 100 log2 1 y 100 log2 1 y 100 y log2 y y log2 100 y log2(2 x) 4(1)(1) 2 x x Graphical support: Interchange x and y. y [ 4, 4] by [ 4, 8] 40. 2x 2 2x x 5 f x 2x(2x 5 (2x)2 5(2x) 1 (x) x 100 x log2 x 100 x Verify. 5 2 log2 (f f 0 2 x) 1 )(x) f log2 x 100 x 2x(0) 100 2x 2x 5 x 0 2 5 1 4(1)(1) ( 5) 2(1) 21 2 1 2log2 100 2 5 log2 x 100 x log2 1 21 2.26 or 2.26 2 100 x x Graphical support: 100 100 x x 1 [ 4, 4] by [ 4, 8] 41. ln y 2t 4 e ln y y e 2t (f 4 42. ln(y 1) ln 2 ln(y 1) x e ln(y 100x 100 x) x 4 e 2t 100x (100 x 1) y 1 y 2xe x ex x f )(x) f 1 1 100 2 ln 2 x ln x ln x 1 ln x ln 2 log2 e x(x)(2) 1 100 100 2 1 x 100 2 x 1 log2 100(1 100 2 x) log2 1 2x log2(2 x) 100 x 29 30 Section 1.5 44. y 50 1.1 1 1 1.1 1.1 x 50 y (b) f ( f (x)) 50 log1.1 y log1.1(1.1 ) 50 y 50 log1.1 y log1.1 f log1.1 1 (x) 46. (a) Amount 1 1 log1.1 50 y y log1.1 y 50 y (b) 8 x 50 x log1.1 x 50 1 )(x) x f log1.1 t x 50 x 0 1 1/x x for all x 0 1 t/12 2 1 1 8 13 2 36 47. 500(1.0475)t log1.1 1.1 8 There will be 1 gram remaining after 36 hours. 50 1 1 t/12 2 1 t/12 2 1 t/12 2 t 3 12 Verify. (f f x, since x 1 x f 1 Interchange x and y: y x x 2) 1 x x (1 x2 50 y ( f (x))2 1 x x x 1 45. (a) f ( f (x)) 1000 x 50 x 1.0475t 2 t ln(1.0475 ) ln 2 t ln 1.0475 ln 2 50 1.1log1.1 1 50 x x t 1 14.936 It will take about 14.936 years. (If the interest is paid at the end of each year, it will take 15 years.) 50 50 ln 2 ln 1.0475 x x 48. 375,000(1.0225)t 50x (50 x 50x 50 x) 1.0225t x 8 3 ln(1.0225t) t ln 1.0225 (f 1 f )(x) f 1 1 50 1.1 t x 1,000,000 8 3 8 ln 3 ln ln(8/3) ln 1.0225 44.081 It will take about 44.081 years. 50 1 1.1 x log1.1 50 50 1 1.1 log1.1 50 1.1 x) 50(1 49. (a) y 2539.852 636.896 ln x (b) When x 75, y 209.94. About 209.94 million metric tons were produced. x (c) 636.896 ln x 400 636.896 ln x 50 2539.852 2939.852 ln x log1.1 1 1.1 x log1.1(1.1x) x x 2939.852 636.896 2939.852 e 636.896 101.08 According to the regression equation, Saudi Arabian oil production will reach 400 million metric tons when x 101.08, in about 2001. ...
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This document was uploaded on 10/31/2011 for the course MAC 2311 at University of Florida.

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