1. The problem statement, all variables and given/known data Suppose that f: R -> R is continuous on R and that lim (x -> [tex]\infty[/tex]+)(f(x) = 0) and lim (x -> [tex]\infty[/tex]-)(f(x)=0). Prove that f is bounded on R 2. Relevant equations I have got the proof of when f is continuous on [a,b] then f is bounded on[a,b] but I'm unsure as to whether I can use this proof for this particular question. 3. The attempt at a solution My attempt is merely the proof I speak of from above.