Your comment was correct 100 years ago. But today it is highly inaccurate. Initially Calculus was developed using the ideas of infinitesimals throughout, although this was not yet fully formalized. The first to ground with mathematical rigor was O believe Cauchy with the epsilon-delta definition of limits. For historical reasons this caught on and is the standard way we introduce students to the subject till today. But since then we have already discovered fully rigorous and zero faith ways to define and work with limits: Robinson's non standard analysis and using nilpotent infinitesimals a la synthetic differential geometry. These provide completely rigorous way to view all the classical intuitions that initially develop the subject and are much easier to work with than the current standard epsilon-delta gymnastics. Unfortunately, mathematicians are very conservative and we tend to stick with the conventional way of doing things way more than we should. In fact a huge part of mathematical community have not fully engaged with the beautiful way of defining and using infinitesimals for calculus, even though it would greatly aid the students learning and intuition and solve the disconnect when working with physics using infinitesimals.