Exceed, surpass, transcend, excel, outdo, outstrip mean to go or to be beyond a stated or implied limit, measure, or degree.
Exceed may imply an overpassing of a limit set by one’s right, power, authority, or jurisdiction or by prescription (as in time or space).
The term may also imply superiority in size, amount, degree, or number according to a given standard or measure.
Surpass often replaces exceed, especially when superiority to a standard or measure is implied. When the intent is to imply superiority in quality (as in virtue, in merit, or in skill) rather than in quantity or extent, surpass is usually preferred to exceed.
Transcend carries so strong an implication of rising across or above a limit or measure that, although it is sometimes used in place of exceed and often in place of surpass.
It is the precise term to use when a higher than human or earthly limit, standard, or measure is implied.
In intransitive use excel implies reaching a preeminence in accomplishment or achievement, but in transitive use it differs little from surpass.
Outdo is less formal than excel or surpass , but it is often preferred when there is the intent to connote the breaking of a previously established record.
Outstrip is often preferred to excel or surpass when one wishes to suggest a race, a competition, or a strenuous effort to get ahead.