How Accurate Is the Binomial Approximation for Small x Values?

[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 don't think its relevant. Small numbers just confuse me...how small is small in any case?

 

[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