Question

Question #24348

Answer 1

For the definition of the limit of a function, please see below.

Explanation:

Let `f` be a function defined on an open interval containing `a` (except possibly at `x=a`)

`lim_(xrarrcolor(green)(a))color(red)(f(x)) = color(blue)(L)` if and only if

for every `epsilon > 0`, there is a `delta > 0` such that:
for all `x`, `" "` if `0 < abs(x-color(green)(a)) < delta`, then `abs(color(red)(f(x))-color(blue)(L)) < epsilon`.