1. The problem statement, all variables and given/known data I am trying to come up with a continuous function in L1[0,infinity) that doesn't converge to 0 as the function goes out to infinity. 2. Relevant equations I am trying to show an example of an f in L1[0,infinity) (i.e. ∫abs(f) < infinity) where the limit as the function goes to infinity does not exist. 3. The attempt at a solution My professor said it could be done in the lecture, but I have had no success... I have been experimenting with decreasing oscillating functions (e.g sinx/x - where I can't stop it converging to 0) and rapid oscillating functions (e.g. sin(e^x) - can't seem to get an integral on the absolute value) and haven't figured it out yet. Anyone have any ideas about a function that would work?