• Suppose she wants to estimate the height atwhich the rock layer 50 million years old, andwants to program her software to use Newton'sMethod to do this approximation. What functioncould she use, that approximating a zero of thatfunction would give her this estimate?

Newton's Method : Consider the assignment of tracking down the arrangements of f(x)=0. In the event…

Answered: Suppose she wants to estimate the…

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Step 1

Newton's Method :

Consider the assignment of tracking down the arrangements of f(x)=0.
In the event that f is the principal degree polynomial f(x)=ax+b, the arrangement of f(x)=0 is given by the equation x=-b/a. In the event that f is the second-degree polynomial f(x)=a{x}^{2}+bx+c, the arrangements of f(x)=0 can be found by utilizing the quadratic formula. Notwithstanding, for polynomials of degree at least 3, observing underlying foundations of f turns out to be more confounded. In spite of the fact that equations exist for third-and fourth-degree polynomials, they are very convoluted. Additionally, assuming f is a polynomial of degree 5 or more noteworthy, it is realized that no such equations exist. For instance, think about the capacity

f(x)={x}^{5}+8{x}^{4}+4{x}^{3}-2x-7.

No recipe exists that permits us to track down the arrangements of f(x)=0. Comparable challenges exist for nonpolynomial capacities. For instance, consider the errand of tracking down arrangements of \tan (x)- x=0. No basic recipe exists for the arrangements of this situation. In cases, for example, these, we can utilize Newton's method to inexact the roots.
Newton's method utilizes the accompanying plan to estimated the arrangements of f(x)=0. By drawing a diagram of f, we can appraise a foundation of f(x)=0. How about we call this gauge {x}_{0}. We then, at that point, attract the digression line to f at {x}_{0}. If {f}^{\prime }({x}_{0})\ne 0, this digression line meets the x-pivot sooner or later ({x}_{1},0). Presently let {x}_{1} be the following guess to the real root. Commonly, {x}_{1} is nearer than {x}_{0} to a real root. Next we attract the digression line to f at {x}_{1}. In the event that {f}^{\prime }({x}_{1})\ne 0, this digression line likewise meets the x-hub, creating another guess, {x}_{2}. We go on thusly, determining a rundown of approximations: {x}_{0},{x}_{1},{x}_{2}\text{,… }.