Try another version of this question What word or phrase best fits in the blank below? "If `lim_(x to a)f(x)=L`, then when `x` is near `a` the corresponding values of `f(x)` are close (________________) to `L`." Box 1: Select the best answer
When considering the statement about the limit of a function as `x` approaches `a`, recall the definition of a limit. The limit of `f(x)` as `x` approaches `a` being equal to `L` means that as `x` gets arbitrarily close to `a`, the values of `f(x)` get arbitrarily close to `L`. This doesn't necessarily mean `f(x)` equals `L` when `x` is near `a`, but rather that it can be as close to `L` as desired, depending on how close `x` is to `a`.
and possibly equal