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lim x ->infinity (e^x/lnx)

I got infinity/0 but is that allowed to be my answer?
what about this one:

limx->infinity (sqrt of x /e^x)

i got 0/infinity for this.

2 answers

on the first, L'Hopitals rule

lim= e^x/ (1/x)= xe^x inf

second: lim= 1/2 (1/sqrtx)*(1/e^x) looks like zero.
For the first one, is it infinity?
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