Limits are conceptually equivalent to infinitesimals. Another way to view it is that a limit is a way to evaluate an equation of infinitesimals.
Epsilon Delta is not our definition of limits, it's the definition of the derivative that uses limits as the "backend". But even using infinitesimals you can use the epsilon-delta definition of the derivative.
Epsilon Delta is not our definition of limits, it's the definition of the derivative that uses limits as the "backend". But even using infinitesimals you can use the epsilon-delta definition of the derivative.