## Calculus confusion

**Calculus: An Intuitive and Physical Approach** by Morris Kline 1977 had something that help me clarify notational issues. On pg 26 he writes:

Even this notation in (22) is somewhat lengthy. Hence mathematicians replace it by a still briefer one. Newton used . Leibnex used . Still another notation was introduced by Lagrange and if Euler’s notation is used then the limit (22) is denoted . Thus

The four notations, are identical in meaning by all fall short of perfection. Newton’s symbolism is concise but poor because the dot above the is often overlooked; moreover it fails to show what the independent variables is. Leibniz’s notation suggests that the limit is a quotient whereas the limit of average speeds definitely is not a quotient … The notation is informative but clumsier than or . … However we shall only use the dot notation when the independent variable is time.

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