I'll only include the step that throws me off unless more info is requested, but this is from LC Evans PDEs book:
$ \displaystyle \lim_{t \to \, 0^+ } \left[ \frac{1}{n\,\alpha(n) \, t^{n-1}} \int_{ \partial{B(x,t)}} u(y) \, dS \; \right] = u(x) $
where $ \partial{B(x,t)} $ denotes a sphere centered at $x $ with radius $t$ and $ n \, \alpha(n) \, t^{n-1}$ denotes the surface area of an n-sphere.
I thought maybe I could apply L'Hopital's, but it didn't seem to get me anywhere.
Thanks for any help.