Q1: Find an approximation "x, " to one of the zeroes of p(x) = x –X -1 usingNewton-Raphson and synthetic division where xo =1 ( using four digit rounding).Q2: Suppose that the Taylor series for a function is11f(x) = x +2x' +÷x' +31-x' +..|4Andg(x) =1- x? + x* – x°+.....consider F(x) = f(x) – xg(x), find the multiplicity of the root x-0.Q3: The following table lists the values of f(x) = Vx accurate to the places given,xe[1.2,1.6]F(x;)1.2Xị1.0951.41.1831.61.265a) Use Nevill's method to approximate f(1.5).b) Find the actual error.

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Answered: Q1: Find an approximation “x, " to one…

Q1: Find an approximation “x, " to one of the zeroes of p(x) = x³ –x -1 using Newton-Raphson and synthetic division where x, =1 ( using four digit rounding).

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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Question

Q1: Find an approximation "x, " to one of the zeroes of p(x) = x –X -1 using
Newton-Raphson and synthetic division where xo =1 ( using four digit rounding).
Q2: Suppose that the Taylor series for a function is
1
1
f(x) = x +
2
x' +÷x' +
3
1
-x' +..|
4
And
g(x) =1- x? + x* – x°
+
.....
consider F(x) = f(x) – xg(x), find the multiplicity of the root x-0.
Q3: The following table lists the values of f(x) = Vx accurate to the places given,
xe[1.2,1.6]
F(x;)
1.2
Xị
1.095
1.4
1.183
1.6
1.265
a) Use Nevill's method to approximate f(1.5).
b) Find the actual error.

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