Determine the recursive formulas for the Taylor method of order 4 for the initial value problem below. Note whether or notafдуy' = 7x-2y, y(0) = 0ƏfLet y'=f(x,y). Find and determine whether or not it is bounded. Select the correct choice below and fill in the answer box to complete your choice.dyafOA. ay(x,y)=is not boundedƏfOB. ay(x,y)=Determine the recursive formula for Xn+1 with step size h.(Type an equation.)is bounded.(Type an equation.)Determine the recursive formula for yn + 1, with step size h.is bounded.

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Answered: of Determine the recursive formulas for…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. Suppose f is twice differentiable on an interval I containing the point x = c. Taylor's remainder theorem (we will see this in more detail later) says that |f(x) - L(x)| ≤ M\x-c|² where L is the linear approximation for f at x = c, M is the maximum of f"(x)| on I and x is close to C. Using this, determine how many digits of accuracy the linear approximation for f(x) = cos(x) at c = 0 approximates cos(0.02). Assume all units are radians.
Q 6 please
7. Use the chain rule to differentiate the following functionswith respect to x. (−3x² + 7x − 4) 2023 = √9 - 4x² (a) y (c) m = √√5 +4√t (b) y (d) q = esin(√5+7x²) =
6. a) For the given function (x) = V1 - x, let x, = 0, x1 Lagrange's polynomial P2(x) of degree at most 2 to approximate f (0.55). Use 3-digit rounding. = 0.4 and x2 = 0.7. Construct a %3D b) Find the absolute error.
Let x = a and x = b be the brackets for a root-finding problem for a scalar function f(x). If 8 = b-a is the size of the original bracket, the size of the interval containing the root after four iterations of the bisection method is (a) 8 (unchanged). (b) 8/4 (c) 6/8 (d) 8/16 (e) not knowable with the given information.
Determine the linear approximation of f(x) = x* at x = 1. а. у 3 4x - 3 O b. y=- 4 x - 3 с. у3 4x +3 O d. Not in the list
6. L Graph y sin z and the Taylor polynomial T₂M+1(x) = M (-1)"2n+1 (2n + 1)! 700 on the interval (-2, 2n) for M = 1, 2, 3, ..., until you find a value of M for which there's no perceptible difference between the two graphs.
1. Find the gradicnt of the following functions (here, i = v-1, and A is a constant) (a) f (x) = 3x. (b) ƒ (x, t) = 4c*² + 7t². (c) ƒ (z) = 623 (d) ƒ (2) = Acikz (e) f (x, y) = Ac k(x²+y²). + 7.
Qu9. For the disease model (M1), suppose that BK 0: 0 0, R(t) > 0. Let us write K-S=2. Show that it is possible to find numbers u₁ and u₂ for which the function L(Z, 1, R)= u₁Z+I+u₂R is a Lyapunov function that proves global stability of the disease-free equilibrium point (Z, 1, R) = (0,0,0).

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