In Problems 25–34 find the half-range cosine and sine expansions of the given function.
25.
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Differential Equations with Boundary-Value Problems (MindTap Course List)
- In 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 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 27–36, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x)) any values of x that need to be excluded. = x. Give 27. f(x) = 3x + 4; g(x) = (x- 4) 28. f(x) = 3 – 2x; g(x) = -(x – 3) 29. f(x) = 4x – 8; 8(x) = + 2 30. f(x) = 2x + 6; 8(x) = ;x - 3 31. f(x) = x' - 8; g(x)· Vx + 8 32. f(x) = (x – 2)², 2; g(x) = Vĩ + 2 33. f(x) = ; 8(x) = 34. f(x) = x; g(x) x - 5 2x + 3' 2x + 3 4x - 3 3x + 5 35. f(x) *: 8(x) = 8(x) 36. f(x) = 1- 2x x + 4 2 - x 1.7 82 CHAPTER 1 Graphs and Functions In Problems 37-42, the graph of a one-to-one function f is given. Draw the graph of the inverse function f"1. For convenience (and as a hint), the graph of y = x is also given. 37. y= X 38. 39. y =X 3 (1, 2), (0, 1) (-1,0) (2. ) (2, 1) (1, 0) 3 X (0, -1) -3 (-1, -1) 3 X -3 (-2, -2) (-2, -2) -하 -하 -하 40. 41. y = x 42. y = X (-2, 1). -3 3 X (1, -1)arrow_forward
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- 1. 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_forwardProblem 2.1 (max, argmax, min, argmin) Let f(x) := (2+ sin(2.x)) and A := [0, 2]. (a) Compute: maxeA f(x) and argmax f(x). XEA (b) Compute: min,eg f(x) and argmin f(x). XEA Compute: argmax |[2 -e-f(x}+5 _ -가 (c) XEA (d) „Compute: argmin [11 – In (2 · f(x) + 5)].arrow_forwardProblem 2.1 (max, argmax, min, argmin) Let f(x) := (2 + sin(2rx)) and A := [0, 2]. (a) Compute: max A f(x) and argmax f(x). XEA XEA (b) Compute: min,A f(x) and argmin f(x). XEA Compute: argmax |[2 ·e(x)+5 _ XEA -가. (c) (d) Compute: argmin [11 – In (2 · f(x) + 5)]. XEAarrow_forward
- * 1.3 • If f(x) = 1. D; = R Rf = {1,0} 2. D; = [1,00) Rf = [0, c0) 3. D; = R R; = {1,–1} 4. D; = [1,00) R; = {1,0} then, %3D %3D %3Darrow_forward.9:18 * 1.1 • If x = -0.8, then [x - 1] = %3D | 1. -2 2. -1 3. -0.8 4. 1 2 O 3 4 * 1.2 The Range of f (x) = v1- x is 1. [-1, 0) 2. (-o, 1] 3. (-00, 0) 4. [0, c0) 1 2 3.arrow_forward6. If f (x) = x - 2, then f (x + h) -f (x) h a. -1 b. 1 c. 0arrow_forward
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