While studying heat equation from PDE by L.Evans, I came across the following limit which I'm not able to prove.
For $n>=1, \delta >0$ ,
$lim_{t \to 0+} \;\;{1 \over t^{n/2}}\;\;\int_{\delta}^{\infty}{e^{-r^2/16t} r^{n-1}}dr = 0$
My approaches have been:
1) take the series expansion of the integrand.
2) use the exponential integral.
But it keeps getting complicated. I want to know if there is a better way to attack this problem .