as always, i'd do the cop out method, and try L'Hopital's rule here (i need to look up the proof for it, it's not fair for me to be using it all the time and not know why it works):
Note that as we try to take the limit, the function goes to , this fulfils the conditions for using L'Hopital's
which confirms Krizalid's answer
We can split the limit because both of them exist (actually they have an indermination, then the entire limit should exists)
The second one is well known (it can be killed with a simple change of variables).
For the first one let's set the limit becomes to
Since and the first limit is equal to 1, and finally