Hi everyone,

I am having difficulties calculating the limit of the following:

$\displaystyle \lim_{x \to 0}\Phi\left(\frac{x(x-1)\sigma^2}{2|x|\sigma}\right)$

with the cumulative standard normal distribution $\displaystyle \Phi(.)$ and $\displaystyle \sigma$ being 0.2 or some other constant.

By numerical approximation I have found the following two solutions: 0.5398 for x approaching zero from the left and 0.4602 for x approaching zero from the right. What is strange to me, is that these two values are relatively far apart from each other.

How I can derive the limit of the above in a non-numerical kind of way?

Thanks already.