Here is a what I call, a non-trivial problem of evaluation of a limit. (Hey, I call it non-trivial because I could only find a longish, brute-force solution as given below. If you have a clever, elegant solution, I would like to learn from you. Just write it down, take a snapshot in your smartphone camera, and post it in comments :-)).
Evaluate
Solution. The above limit can be recast as follows:
=
Now, observe as ,
also tends to zero.
So, let . Hence, the required limit is equal to
= call this A but we know that
Hence, the above expression A becomes
=
=
=.
So, what do you think — is there an alternate elegant solution to my brute force solution above? if you have, please share it with me also.
More later…
Nalin Pithwa