Convergence in space of all square integrable functions on [-1,1]

**Problem:**

1. Given the sequence and function . show that

in

2. How can we use this to deduce that (with the max norm) is not complete.

**Pathetic Attempt:**

1.

because .

2. The limit isn't in C[-1,1] so its not complete...

Very bad I know.

Any suggestions are welcome.

Re: Convergence in space of all square integrable functions on [-1,1]

A somewhat better attempt:

I split the integral up in two for simplicity.

Let n go to infinity and we have proved convergence.

Still working on the other part though.