Show that the function 1/t is not in L2 (0,1] Need some help getting started with this problem:
$$f(t) = \frac{1}{t}$$
Show that $f(t)$ is not in $L_2(0,1]$, but that it is in the Hilbert space $L_{2}w(0,1)$ where the inner product is given by $$\langle x,y\rangle = \int(x(t)\overline{y(t)}w(t)dt$$   where  $w(t)=t^2$.
I am thinking that I have to show that the function is continuous over the interval.

SOME HELP: $\int 1/t^2\,dt$ is divergent on $(0,1]$.
