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In Problems 37‒40 proceed as in Example 6 to solve the given initial-value problem. Use a graphing utility to graph the continuous function y(x).
38.
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Chapter 2 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
- In Problems 11–20, for the given functions f and g. find: (a) (f° g)(4) (b) (g•f)(2) (c) (fof)(1) (d) (g ° g)(0) \ 11. f(x) = 2x; g(x) = 3x² + 1 12. f(x) = 3x + 2; g(x) = 2x² – 1 1 13. f(x) = 4x² – 3; g(x) = 3 14. f(x) = 2x²; g(x) = 1 – 3x² 15. f(x) = Vx; 8(x) = 2x 16. f(x) = Vx + 1; g(x) = 3x %3D 1. 17. f(x) = |x|; g(x) = 18. f(x) = |x – 2|: g(x) x² + 2 2 x + 1 x² + 1 19. f(x) = 3 8(x) = Vĩ 20. f(x) = x³/2; g(x) = X + 1'arrow_forwardIn Problems 23–30, use the given zero to find the remaining zeros of each function. 23. f(x) = x - 4x² + 4x – 16; zero: 2i 24. g(x) = x + 3x? + 25x + 75; zero: -5i 25. f(x) = 2x* + 5x + 5x? + 20x – 12; zero: -2i 26. h(x) = 3x4 + 5x + 25x? + 45x – 18; zero: 3i %3D 27. h(x) = x* – 9x + 21x? + 21x – 130; zero: 3 - 2i 29. h(x) = 3x³ + 2x* + 15x³ + 10x2 – 528x – 352; zero: -4i 28. f(x) = x* – 7x + 14x2 – 38x – 60; zero:1 + 3i 30. g(x) = 2x – 3x* – 5x – 15x² – 207x + 108; zero: 3iarrow_forwardIn Problems 19–30, graph the function f by starting with the graph of y = x² and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f(x) = a(x – h)² + k.] 19. f(x) = 20. f(x) = 2x2 + 4 21. f(x) = (x + 2)² – 2 22. f(x) = (x – 3)² – 10 23. f(x) = x² + 4x + 2 24. f(х) — х? — бх — 1 25. f(x) = 2x? – 4x + 1 26. f(x) = 3x? + 6x 4 27. f(x) = -x² - 2x 28. f(x) 3D-2х? + 6х + 2 29, f(x) : 30. f(x) 1 + xarrow_forward
- In Problems 2–4, for the given functions fand g find: (a) (f° g) (2) (b) (g • f)(-2) (c) (fo f) (4) (d) (g ° 8) (-1) 2. f(x) = 3x – 5; g(x) = 1 – 2r 3. f(x) = Vx + 2: g(x) = 2x² + 1 4. f(x) = e"; g(x) = 3x – 2arrow_forwardIn Problems 23–28, answer the questions about the given function. x² + 2 26. f(x) = x + 4 23. f(x) = 2x? - x - 1 (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -1, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. 24. f(x) = -3x² + 5x (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. x + 2 (a) Is the point ( 1,) on the graph of f? (b) If x = 0, what is f(x)? What point is on the graph of f? (c) If f(x) =5. what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if…arrow_forwardIn Problems 29–40: (a) Find the domain of each function. (d) Based on the graph, find the range. (b) Locate any intercepts. (e) Is f continuous on its domain? S3x 14 (c) Graph each function. S2r 29. f(x) : if x + 0 S-2x + 3 3x – 2 if x 1 x + 3 2x + 5 if -3 sx0 S1 + x if x 0 35. f(x) : 36. f(x) = 37. f(x) if x 20 S2 - x if -3 sx1arrow_forward
- 23. What is the domain of the function f(x) = Vx² – 16? %3D In Problems 25–32, use the given functions f and g. (a) Solve f(x) = 0. (e) Solve g(x) s 0. (b) Solve g(x) = 0. (f) Solve f(x) >g(x).arrow_forwardIn Problems 33–44, determine algebraically whether each function is even, odd, or neither. 34. f(x) = 2x* –x? 38. G(x) = Vĩ 33. f(x) = 4x 37. F(x) = V 35. g(x) = -3x² – 5 39. f(x) = x + |x| 36. h (х) — Зx3 + 5 40. f(x) = V2r²+ 1 x² + 3 -x 42. h(x) =- 1 2x 44. F(x) 41. g(x) 43. h(x) x2 - 1 3x2 - 9arrow_forwardIn Problems 23–30, use the given zero to find the remaining zeros of each function.arrow_forward
- In Problems 43–66, find the indicated extremum of each function on the given interval.arrow_forward1. If f(x) is a function such that f(1) = 2, f(n + 1) = (3f(n)+1)/3 for n = 1, 2, 3, ..., what is the value of f(100)?arrow_forward4. Suppose the following functions are a general solution of: y(4) + a3y" +a2y" + a1y' + a0y = 0arrow_forward
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