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.
(..) I'll even shake hands. Bark, bark? So, without a family of my own... I dedicated myself to the pursuit of knowledge... Yay! And then, I devoted myself to helping mankind. I pioneered new techniques in alternative energy. (..)2014 Mr. Peabody & Sherman