Question:

Consider a cube with side length 1 and vertices A, B, and C as indicated in the illustration below: A B 1 C 1. Find the exact le

Consider a cube with side length 1 and vertices A, B, and C as indicated in the illustration
below:
A
B
1
C
1. Find the exact length of the line segment AB.
2. Find the exact length of the line segment AC.
3. Find the exact area of the triangle AABC.
(Note: “exact” means that if it is a radical, you should use radical notation. Do not
approximate.)

Consider a cube with side length 1 and vertices A, B, and C as indicated in the illustration below: A B 1 C 1. Find the exact length of the line segment AB. 2. Find the exact length of the line segment AC. 3. Find the exact area of the triangle AABC. (Note: “exact” means that if it is a radical, you should use radical notation. Do not approximate.)

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874
CHAPTER 11 INTEGRATION
7.
24. JA) = +", "(8) - 1.6 - 3
25. S(x) = 2,901) - 1,6-2
26. f(x) = 4.9(x) = a = 1.b - 3
In Exercises 27-34, sketch the graph, and find the area of the
region bounded by the graph of the function f and the lines
y=0, x=a, and x=

Math

Area Solutions

874 CHAPTER 11 INTEGRATION 7. 24. JA) = +", "(8) - 1.6 - 3 25. S(x) = 2,901) - 1,6-2 26. f(x) = 4.9(x) = a = 1.b - 3 In Exercises 27-34, sketch the graph, and find the area of the region bounded by the graph of the function f and the lines y=0, x=a, and x=b. 27. f(x) = 3; a = -1, b = 2 28. f(x) = 6 - 2x; a = -1, b = 1 29. S(x) = -x + 4x - 3: a = -1, b = 2 30. f(x) = -x: a = -1, b = 1 31. f(x) = x - 4x2 + 3x; a = 0, b = 2 32. f() = 4x + x4, a = -1, b = 8 33. f(x) = -1; a = -1, b = 3 34. f(x) = xe;a = 0, b = 2 8. y=+6 os 4 -3 -2 In Exercises 9-16, sketch the graph, and find the area of the region bounded below by the graph of each function and above by the x-axis from x = a to x = b. 9. f(x) = -x?: a = -1, b = 2 10. f(x) = x2 – 4; a = -2, b = 2 11. f(x) = x2 - 5x + 4; a = 1, b = 3 12. $(x) = x; a = -1, b = 0 13. f(x) = -1 - Vx; a = 0, b = 9 In Exercises 35-42, sketch the graph, and find the area of the region completely enclosed by the graphs of the given func- tions fand g. 35. f(x) = x + 2 and g(x) = x2 - 4 36. f(x) = -x² + 4x and g(x) = 2x - 3 37. f(x) = x² and g(x) = x3 38. f(x) = x + 2x2 – 3x and g(x) = 0 39. f(x) = x3 - 6x2 + 9x and g(x) = x2 – 3x 40. f(x) = Vx and g(x) = x2 41. f(x) = xV9 - x? and g(x) = 0 42. f(x) = 2x and g(x) = xVx + 1 14. f(x) = 3x - Ve; a = 0, 6 = 4 15. f(x) = -e(12); a = -2, b = 4 16. f(x) = -xe-f; a = 0, b = 1 In Exercises 17-26, sketch the graphs of the functions fand 9, and find the area of the region enclosed by these graphs and the vertical lines x = a and x = b. 17. f(x) = x2 + 3.9(x) = 1; a = 1, b = 3 18. f(x) = x + 2, g(x) = x2 - 4; a = -1, b = 2 19. f(x) = -x2 + 2x + 3,9(x) = -x + 3; a = 0, b = 2 20. f(x) = 9 - x?, g(x) = 2x + 3; a = -1, b = 1 43. EFFECT OF ADVERTISING ON REVENUE In the accompanying fig- ure, the function f gives the rate of change of Odyssey Travel's revenue with respect to the amount x it spends on advertising with their current advertising agency. By engaging the services of a different advertising agency, it is expected that Odyssey's revenue will grow at the rate given by the function g. Give an interpretation of the area A of the region S and find an expression for A in terms of a definite integral tivoling fand g. R=g(x) Dollars/dollar R=f(x) 21. f(x) = x2 + 1,9(x) = 5x*; a = -1, b = 2 22. f(x) = V8, 9(x) = x - 1; a = 1, 6 = 4 23. f(x) = 1.5(x) = 0 b Dollars = 2x - 1; a = 1, b = 4 Unless otherwise noted, all content on this page is © Cengage