In Problems 25–34 find the half-range cosine and sine expansions of the given function.
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Differential Equations with Boundary-Value Problems (MindTap Course List)
- 1. In the figure below, find the number(s) "c" that Rolle's Theorem promises (guarantees). 10 For Problems 2–4, verify that the hypotheses of Rolle's Theorem are satisfied for each of the func- tions on the given intervals, and find the value of the number(s) "c" that Rolle's Theorem promises. 2. (a) f(x) = x² on |-2, 2 (b) f(x) = x² =5x +8 on [0,5] 3. (a) f(x) = sin(x) on [0, 7] (b) f(x) = sin(x) on [A,57]| 4. (a) f(x) = r-x+3 on | 1,1] (b) f(x) = x cos(x) on (0, [0, 1arrow_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 13–22, for the given functions f and g, find:(a) (f ∘ g) (4) (b) (g ∘ f) (2) (c) (f ∘ f) (1) (d) (g ∘ g) (0)arrow_forward
- Problem 13 (#2.3.10).Determine whether each of these functions from {a,b,c,d} to itself are one-to-one. a) f(a) = b, f(b) = a, f (c) = c, f(d) = d, b) f(a) = b, f(b) = b, f(c) = d, f(d) = c, c) f(a) = d, f(b) = b, f (c) = c, f (d) = d.arrow_forward.4 Evaluate J2 sec -1 Va drarrow_forwardProblem 4. Let f and g be functions on [a, b], and assume that f(a) = 1 = g(b) and f(b) = 0 = g(a). Show that {f,g} is independent in F[a, b].arrow_forward
- . Eliminate the - arbitrary constants C, and C, y= Ge*• C,e" + ± y =arrow_forwardto STUDENTS of 5さ WHAT FUNCTION =C(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_forward
- Question 3 Differentiate the following with respect to X: In(x? +3x +5) X O A. <²+3x +5 .2 В. 2x +3 x² +3x +5 X Oc. x² +3x +5 O D. 2х+8 x² + 3x +5 .2 3.arrow_forwardQuestion 10. Plot the result of the following convolution X₁(t) 0 2 4 * X2(t) 0 2 6arrow_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
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