Calculus helps us to understand and analyze the behavior of functions more precisely than using infinitesimals by providing a more rigorous and formal framework. Using calculus, we can calculate derivatives and integrals of functions, which give us important information about the behavior of the function. For example, derivatives tell us the rate of change of a function at a particular point, while integrals give us the total area under the curve of a function.


In addition, calculus provides us with powerful techniques for solving optimization problems and modeling real-world phenomena. For instance, we can use calculus to optimize the design of bridges and buildings, model the spread of diseases, and predict the motion of planets and satellites.


While infinitesimals were originally used as a way of thinking about calculus problems, they were not well-defined mathematically until later. In contrast, the techniques and concepts of calculus are well-defined and widely accepted in modern mathematics, making it a more reliable and rigorous approach to studying the behavior of functions.
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