Lp Space functions?

Question

find a continuous function in [0, infinity) that is in L1 but not in L2.

Answer 1

f(x)=-1 if 0<=x<1,
=(-1)^n/sqrt(n)*(1-x+n)
+(-1)^(n+1)/sqrt(n+1)*(x-n) if n<=x
This is basically the polygonal function formed by connecting the points
(0,-1),(1,-1),
(2,1/sqrt(2)),(3,-1/sqrt(3)),
(4,1/sqrt(4)),...