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

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