Consider the Ivp:Using the Euler method with a time step of At= 0.5 approximate x(1.5) to the nearest thousands6-Pplaces.8 +2.0.2.0+1OPx² + 4tx=0x(0)=-1, x²(0)=-32sPcs Scanned with CamScanner

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Answered: Consider the Ivp: x²+4+x=0 x(0)=-1,…

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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Determine the unknown values in the table if the problem requires the root of f(x) using bisection method using an initial guess of xl = -5 and xu = -4 f(x) = x2 + 4x Iteration xl xu f(xl)f(xr) xr e3 1 -5 -4 -4.5 0.75 2 A В C -5 -4.75 -4.5 -4.25 -4 5.88% 5.56% 5.26% A В
Q7
Given the function : f(x) = x³ + 5x² + 7x − 20; solve using Bisection Method with initial values of (1.000, 2.000) 1st iteration xn = 1.000 xp = 2.000 xnew = 1.500 2nd iteration xn = 1.000 xp = 1.500 xnew = 1.250 3rd iteration xn = 1.250 xp = 1.500 xnew = 1.375 4th iteration xn = 1.250 xp = 1.375 xnew = 1.312 5th iteration xn = 1.250 xp = 1.312 xnew = 1.281 f(xn) = -7.000 f(xp) = 22.000 f(xnew) = 5.125 f(x) = -7.000 f(xp) = 5.125 f(xnew) = -1.484 f(xn) = -1.484 f(xp) = 5.125 f(xnew) = 1.678 f(xn) = -1.484 f(xp) = 1.676 f(xnew) = 0.049 f(x) = -1.484 f(xp) = 0.049 f(xnew) = -0.726
Approximate the root of the equation √x + x² = 7 using the initial value xo = 2-3 and using the 4th iteration of the numerical method: bisection method
LETTER C ONLY. DO NOT ROUND OFF
A town’s population is growing according to the function P(t) = 200 - 14t + 3t2, where P(t) denotes the town’s population after t weeks for (0 < t < 20). How fast will the population be increasing 1 week from now?
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Iterate towards an extreme value of the function B(x) using the quadratic interpolation. Use the initial values xo = -2.2- 2-₁, x₁ = 0, X₂ = 8. Calculate three iterations. S = 9 B(x)=ex/2 + -X S+2 9
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T(n) = 2T(n − 1) + 1, T(0) = 1. Use the iteration method to find a () evaluation for T(n).

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Consider the Ivp: x²+4+x=0 x(0)=-1, x²(0) = -3 Using the Euler method with a time step of At = 0.5 approximate x(1.5) to the nearest thousands -P places. 8+2.0- 2.0+1 2st