For the first one, define so
For the second one, you can take it more generally:
the previous solution was also the first thing that came into my mind, yet your teacher didn't want it that way.. i haev another approach..
we know that thus if we let , then we have
, and take the limit as so it becomes
and the limit part is in the case of , you may use L'hospital's Rule, so the limit part equals 1 and so ..
you can do the same thing for 2..