As you said, this is equivalent to
Now would be a good time to use L'Hopital's rule, if you have learned this. Have you?
Hello,Originally Posted by tnkfub
here is a way to solve this problem without using the l'Hospital rule:
Substitute the x by (1+1/n) and calculate the limit for n approaching infinity:
After a few steps of very unpleasant transformation you'll get:
Hello,Originally Posted by ThePerfectHacker
honestly speaking: No.
1. When you calculate the derivative you calculate for instance the limit
2. I made an analoguous conclusion to use this method with this problem. I noticed that it worked fine. But of course that isn't a proof.