〜限り（は）

私(わたし)の知(し)る限(かぎ)り、彼(かれ)は来(き)ません。

Watashi no shiru kagiri, kare wa kimasen.

As far as I know, he is not coming.

知る限り fences the claim inside what you know — a hedge

体(からだ)が元気(げんき)な限(かぎ)り、働(はたら)き続(つづ)けます。

Karada ga genki na kagiri, hataraki tsuzukemasu.

I will keep working as long as I am well.

The second sense is for as long as that holds

できる限(かぎ)り早(はや)く返事(へんじ)します。

Dekiru kagiri hayaku henji shimasu.

I will reply as soon as I possibly can.

できる限り has settled into a fixed adverb meaning as much as possible