also: できうるかぎり
expression
as much as possible; as far as possible
Used to express doing something to the greatest extent one can. Often interchangeable with できるだけ, but できる限り can sound slightly more formal or emphatic.
出来る限り早く返事をください。
Please reply as soon as possible.
できる限りのことはしたつもりです。
I believe I did everything I could.
More common and slightly more casual than できる限り. Both mean 'as much as possible', but できる限り can carry a nuance of 'to the utmost limit'.
Combination of the potential form of する (できる, 'can do') and 限り (かぎり, 'limit'). The variant できうる uses the classical potential verb 得る (うる) for emphasis.