In Problems 1–4 construct a table comparing the indicated values of y(x) using Euler’s method, the improved Euler’s method, and the RK4 method. Compute to four rounded decimal places. First use h = 0.1 and then use h = 0.05.
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Differential Equations with Boundary-Value Problems (MindTap Course List)
- Problem. 9: Let z = x? 7 xy + 6 y? and suppose that (x, y) changes from (2, 1) to (1.95, 1.05 ). (Round your answers to four decimal places.) (a) Compute Az. (b) Compute dz. ?arrow_forwardIn Problems 47–58, use a calculator to solve each equation on the interval 0 … u 6 2p. Round answers to two decimal places. 47. sin θ = 0.4 48. cos θ = 0.6 49. tan θ = 5 50. cot θ = 2 51. cos θ = - 0.9 52. sin θ = - 0.2 53. sec θ = - 4 54. csc θ = - 3 55. 5 tan θ + 9 = 0 56. 4 cot θ = - 5 57. 3 sin θ - 2 = 0 58. 4 cos θ + 3 = 0arrow_forwardFigure attached below. 1. A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at atime, until the defective ones are identified. Denote by X the number of tests made until the first defectis identified and by Y the number of additional tests until the second defect is identified.(a) Find g(x|y) and draw a figure like Figure 4.3-1(b), depicting the conditional pmfs fory = 1,2,3,and 4.(b) Find h(y|x) and draw a figure like Figure 4.3-1(c), depicting the conditional pmfs forx = 1,2,3,and 4.(c) Find E [X|Y = 2] and Var (X|Y = 2)arrow_forward
- In Problems 39–46, show that (f ° g) (x) = (g° f) (x) = x. %3D 39. f(x) = 2x; g(x) = 40. f(x) = 4x; g(x) = i* 41. f(x) = x; g(x) %3! %3D 43. f(x) = 2x – 6; 8(x) = ; (x + 6) 46. fl+) = s(*) = 42. f(x) = x + 5; g(x) = x - 5 44. f(x) = 4 – 3x; g(x) = (4 - x) %3D 45. f(x) = ax + b; g(x) = - (x - b) a + 0 %3D aarrow_forwardIn Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 3. x" + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375, x'(0) = 0arrow_forward1. Solve for the orthogonal trgsctories y² = 4x*(1- kx) %3Darrow_forward
- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 4. x" + 25x = 90 cos 41; x (0) = 0, x'(0) = 90arrow_forward4.x2 — 6х + 2у —8 %3D0 at x %3D 3arrow_forwardObtain characteristics for y2 Uxx + Uyy = %3Darrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage