Since I haven't learned to use LaTex yet, for convenience, let L.H.f(x) be the limit of f as x approaches c from the left.
1.) If f(x)>0 and L.H.f(x) = 0, show that L.H.(1/f(x)) = infinity.
2.) Give an example of a function f for which L.H.f(x) = 0, but L.H.(1/f(x)) is neither infinity nor negative infinity.
Thanks for your quick response. I was thinking the proof would be similar to yours, but I wasn't sure if that reasoning alone would be rigorous enough (this is for an analysis class). I was thinking I needed to use the epsilon-delta definition in my proof.