Question

Estimate sqrt[3]{10} using newton method. Take x1 = 2 as initial guess.

Answer 1

It specifies to work with fractions, eg: x2 (which is really x1 if you consider initial to be xo) = ? / 6, x3 = ? / 1521

Answer 2

Anyone?

Answer 3

so

\[f(x) = x^3 - 10\] f(2) = -2

\[f'(x) = 3x^2\] f'(2) = 12

\[x _{1} = 2 - (-2)/12\]

\[x _{1} = 2 1/6\]

Answer 4

oops \[x _{1} = 13/6\]

Answer 5

How do you even know to start with x^3 - 10? What's the math / algebra behind it, I'm curious.

Answer 6

I've run into a problem for my second x, I end up with: x2 = (13/6) - (37/216) x (36/507). How do I simplify that? No matter how I try I end up getting 13/6 - (18.5/1521). Doesn't really make sense.