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.
(..) by the way. And you turn us down out of pride, whatever... ...and then you tell your wife that in fact we are paying for your treatment. Without our knowledge, against our will... ...you involve us in your lie. And you sit here and tell me that that is none of my business? Yeah. (..)2009 TvShow: Breaking Bad Title: Peekaboo Season: 2 Episode 6