A graph of ƒ and the lines tangent to ƒ at x = -3, 2, and 3 aregiven. If x0 = 3, find the values of x1, x2, and x3 that are obtainedby applying Newton’s method. 2.y= fx)-42.

Name: A graph of ƒ and the lines tangent to ƒ at x = -3, 2, and 3 aregiven.
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Description: A graph of ƒ and the lines tangent to ƒ at x = -3, 2, and 3 aregiven. If x0 = 3, find the values of x1, x2, and x3 that are obtainedby applying Newton’s method. 2.y= fx)-42.

Answered: 2. y= fx) -4 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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Question

A graph of ƒ and the lines tangent to ƒ at x = -3, 2, and 3 are
given. If x₀ = 3, find the values of x₁, x₂, and x₃ that are obtained
by applying Newton’s method.

Expert Solution

Step 1

Given: A graph of ƒ and the lines tangent to ƒ at x = -3, 2, and 3.

To Find: $x_{1}, x_{2}, and x_{3}$ by applying Newton's method.

Step 2

In Newton's Method:

Let $x_{0}$ be the initial approximation

We draw a tangent line at $x_{0}$ ,

The point at which the tangent cuts the x-axis is our new approximation( name it $x_{1}$ ).

So, $x_{1}$ is our next root.

Now, Again we draw a tangent line at $x_{1}$ ,

the point at which it cuts the x-axis is our new approximation (name it $x_{2}$ )

So, $x_{2}$ is our next root.

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