Procedure for Newton’s Method

1. Guess a first approximation to a solution of the equation . A graph

of may help.

2. Use the first approximation to get a second, the second to get a third, and so

on, using the formula

Example:

So to find a positive root of this equation

we have to guess a value of . It doesn't have to be exact.

Let so becomes if we plugin this into (1) and after simplification we get:

The graph of is:

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Figure 1

Let's guess a approximate value where the graph of so from the graph(Figure 1) say where and plug in into equation (2) and solve for and then plug-in and find and this goes on until you get a good approximation up to a particular decimal places:

And that's it. You approximated the positive root of to five decimal places.