limit as x approaches zero

Hi everyone,

I am having difficulties calculating the limit of the following:

with the cumulative standard normal distribution and 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.

Re: limit as x approaches zero

and . In other words, has a jump discontinuity at x = 0, so it is not surprising that the composition of this function with a continuous function also has a jump discontinuity.

Re: limit as x approaches zero

Hi Emakarov,

Thank you. Very good help.

Bests