<human>:  When did the concept of a limit come into mathematical analysis?
<bot>: The concept of a limit was introduced by Leibniz in 1687. Before Leibniz, mathematicians had to make use of infinitesimals in order to prove their theorems. This was not a very good solution because infinitesimals were not rigorously defined, and it was difficult to use them in proofs. The limit was introduced as a way to avoid the use of infinitesimals. The concept of a limit has been extremely useful in the study of calculus, and has led to many important theorems.