I found this question in Gelman's Bayesian Data Analysis's chapter on Asymptotics.
Assume you have two independent random variables $X$ (with mean 4 and standard deviation 1) and $Y$ (with mean 3 and standard deviation 2). How do you approximate the mean and standard deviation of $Y/X$? Under what assumptions is the approximation reasonable?
I tried to approximate these random variables as Normal with sample size large enough, but this requires calculating $E(Z^{-1})$ and other negative moments of a Normal distribution, and I think these integrals don't converge.