## SEEMOUS 2012 Problem 4

a) Compute .

b) Let be an integer. Compute

.

a) Make the change of variable . The limit becomes

Prove first that if is continuous then . This can be done in several steps as follows:

- Prove it first for functions of the form .
- Extend it easily to polynomials.
- Approximate uniformly by polynomials to get the desired result.

For b) something similar works, but it is more intricate. I will come back with the details.

Advertisements

Categories: Analysis, Olympiad, Problem Solving
integral, limit

Comments (0)
Trackbacks (0)
Leave a comment
Trackback