Evaluating ln(x + sqrt[1+x2]) - sin(x) at x=.001

[psyklon]

Homework Statement

The problem I'm attempting to solve asks you to evaluate the function at a given point. In this case:

ln(x + sqrt[1+x²] ) - sin(x)
@ x = .001

Homework Equations

sin(x) = x - (x³/3!) + (x⁵/5!) - (x⁷/7!) + ...
AND
ln(1 + x) = x - (x²/2) + (x³/3) - (x⁴/4) + ...

The Attempt at a Solution

I know I'm supposed to substitute in the power series expansions, but I'm not sure how to begin modifying the second expansion to suit my needs in solving the problem. Can anyone point me in the right direction?

 

[rock.freak667]

Since x is small, you can approximate sin(x) as just x, you can do the same with the other functions.