Try another version of this question What word or phrase best completes the sentence below? "If `lim_(x to a)f(x) ne L`, then we can find an `epsilon>0` so that no matter how close `x` is to `a`:" Box 1: Select the best answer
Think about the definition of a limit in terms of `epsilon` and `delta`. If `lim_(x to a)f(x) ne L`, it implies that there exists an `epsilon>0` such that for every `delta>0`, there are values of `x` within `delta` of `a` where `∣f(x)−L∣≥ϵ`. This means `f(x)` fails to be arbitrarily close to `L` within any neighborhood around `a`.
it is possible for `f(x)` to be at least `epsilon` units away from `L`.