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
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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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.