1Consider the roots (zeros) of f(x) =a³ – 4x + 1.7+6-5-4--4-3-23-1--2--3-4-5+We will see that small changes in the choice of x, produce different roots, or none at all.For each x, given, state the root (zero) of f(x) to which the algorithm converges, or writeDNE if it does not converge.round to 3 decimal placesIf x, = 1.85, then Newton's Method converges to: x =If r.1.7, then Newton's Method converges to: * =If To1.55, then Newton's Method converges to: 2 =3.

Given, f(x)=13x3-4x+1f'(x)=x2-4by newton's method xn+1=xn-f(xn)f'(xn)x0=initial guess

Consider the roots (zeros) of f(x) = a³ – 4x + 1. 7+ 6 5 3 -4 -3 -2 -1 3 -1 -2 - -3 - -4 -5- We will see that small changes in the choice of r, produce different roots, or none at al For each r. given, state the root (zero) of f(x) to which the algorithm converges, or w DNE if it does not converge. round to 3 decimal places If x, = 1.85, then Newton's Method converges to: # = If x, = 1.7, then Newton's Method converges to: æ = If x, = 1.55, then Newton's Method converges to: x = 2.

Consider the roots (zeros) of f(x) = a³ – 4x + 1. 7+ 6 5 3 -4 -3 -2 -1 3 -1 -2 - -3 - -4 -5- We will see that small changes in the choice of r, produce different roots, or none at al For each r. given, state the root (zero) of f(x) to which the algorithm converges, or w DNE if it does not converge. round to 3 decimal places If x, = 1.85, then Newton's Method converges to: # = If x, = 1.7, then Newton's Method converges to: æ = If x, = 1.55, then Newton's Method converges to: x = 2.

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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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

1
Consider the roots (zeros) of f(x) =a³ – 4x + 1.
7+
6-
5-
4-
-4
-3
-2
3
-1-
-2-
-3
-4
-5+
We will see that small changes in the choice of x, produce different roots, or none at all.
For each x, given, state the root (zero) of f(x) to which the algorithm converges, or write
DNE if it does not converge.
round to 3 decimal places
If x, = 1.85, then Newton's Method converges to: x =
If r.
1.7, then Newton's Method converges to: * =
If To
1.55, then Newton's Method converges to: 2 =
3.

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