I answered their questions 'to the best of my knowledge'. [=I gave the best answers I could based on what I knew, but I might have answered differently if I had known something else]
No one arrived late 'to my knowledge'. [=I am not aware that anyone arrived late, but it is possible that someone arrived late and I don't know about it]
They went on vacation, 'safe in the knowledge' that the farm would be well cared for while they were away.
(..) Follow me! Okay. So we do here is we get the target with a quick fly over. We just the trajectory in the land dead center. Am I missing anything, Rhino? Just the knowledge that every minute spent in your company becomes... ...the new greatest minute of my life! No, forget it! How do you say, (..)2008 Bolt