1. The problem statement, all variables and given/known data I've to show that if f:R->R is continuous in x' then f is limited in a suitable environment of x'. 2. The attempt at a solution My lecturer said we should use the following inequality |f(a)|=<|f(a)-f(y)|+|f(y)| But how should I go on, I know I have to show something like this: It exists d>0: it exist c element of [x'-d, x'+d]=I ==> |f(x)|=<|f(c)| for every x in I. But how should I go on?