Question

Use Newton's Method to approximate the root of x ln x=2 accurate to five decimal places. Begin by sketching a graph.

Answer 1

Newton's method as in linear approximation (i.e. first degree differentiation)?

Answer 2

x1 = x0 - f'(x) / f(x)

Answer 3

first thing is to define f(x)=xlnx -2
and you want to find where f(x)=0
The Newton method works with the tangent line, so you need to derivative of the function.
f'(x)=lnx +1
The tangent line is this, where m=f'(x)
y-y0 = m(x-x0)
y = m(x-x0)+y0

I think everything is here to do it. You just have to do a few steps to get it to 5 decimal places.

Answer 4

\[f(x) = x0 + f'(x0)(x-x0)\]

using this you get the new value for x0 and plug it in the same eq.

Answer 5

i dont have a calculator will one of you get me a decimal please?

Answer 6

you have a computer. There is a default calculator

Answer 7

1.41421

Answer 8

cralli:I have to agree with andras the site is not meant to get other people to do your work.You have to try it on your own.If you have problems...its cool.... just show us where you got till.