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## Homework Statement

Given two functions; y= ln(x) and y=(x^2)/8 - 2

Use Newton's Method to approximate all intersection points of the given functions, each with 3 decimal places.

## Homework Equations

Xn+1 = Xn - f(x) / f`(x)

## The Attempt at a Solution

__I equated the two equations, and I got__

**Step 1:**f(x) = ln(x) - (x^2)/8 +2

__Step 2:__I found the derivative as f`(x) = 1/x - x/4

__then I drew the graphs, and I found that they only intersect at a point near 5.4 (because ln(x) doesn't have any graph in the -x direction)__

**Step 3:**so I started off x1 = 5.4 and then using the equation given above I found the following values:

X2 = 5.435

X3 = 5.436

X4 = 5.435

X5 = 5.436

Can you guys please tell me if I did the solution right and at which point do I stop ... they keep going ... I'm not going same 3 decimal places for any of them ?

I hope someone would answer soon because I have it due tomorrow early morning. Thanks and can you also tell that whatever I did was right and nothing else was to be done!

Thanks