Hi all, I'm looking for a positive real-valued function definition on all of R such that the function f(x) is continuous and integrable (the improper integral from -infinity to infinity exists and is finite) but that lim sup f(x)=infinity as x goes to infinity. I'm thinking about something with spikes of decreasing width but I'm not sure how to get an exact formula for the function or if this is the right idea. Any help is much appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculus Counterexample

**Physics Forums | Science Articles, Homework Help, Discussion**