What is the difference between these three adverbs: extremely, exceedingly and keenly?

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I am keenly aware that he was going extremely fast exceeding the speed limit by over 30kph.

Sorry couldn't squeeze exceedingly in...

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Oxword dictionary: 
extremely(it is used mostly with adjectives and adverbs) - to a very high degree - extremely important, useful, complicated. 
exceedingly( formal which is becoming old-fashioned) - extremely, very, very much.
keen - wanting to do sth or to happen sth very much, enthusiastic about activity, idea.