What we have is,

If the function fails to be continous at (it is continous everywhere else because the product of two continous functions at a point is continous at that point).

So what is the limit,

equal to?

If, then,

.

And we have discontinuity be the limit

Does not exist.

So we need to consider the cases when .

We require the limit from the right to conincide with the limit from the left. Since is always positive and does change from positive and negative. We can only have for limit existence to be 0. Which is persicely what the functional value at the point is, .

Thus, we can consider cases when the right-handed limits are zero.

In that case,

We can write,

(But that limit does not exist, ever.

If you appraoch it a even or odd multiplies of )*

*)I did not prove that, but it makes sense to me.