# Homework Help: Binomial Approximations

1. Oct 18, 2005

### Bucky

Show that if x is small then

1/(1+x) - root(1-2x) ~= (3/2)x^2

im not sure how to even begin this question. there was a part 1 but i dont think its relevant. Small numbers just confuse me...how small is small in any case?

2. Oct 18, 2005

### HallsofIvy

You titled this "binomial Approximations"- obviously you are intended to expand both $\frac{1}{1+x}= (1+x)^{-1}$ and $\sqrt{1- 2x}= (1-2x)^{\frac{1}{2}}$ using the binomial formula. Then drop higher powers since if x is small, x to a power is much smaller.
"how small is small in any case?" Well, in this case, small enough that the third power is negligible- because you were asked to show that this is approximately a number times x2