(1) Asymptotes are lines in graphical geometry which represent the limit(s) of a curve, that is, the asymptote represents a boundary which a curve approaches but never touches or breaches.
(2) Limits are fundamental to the study of the behaviour of functions. For a function f(x) there may be values of x for which the function is undefined, but by considering values of x approaching one such value (either from the negative or the positive side of the value) there can be finite values for such limits.
(3) In calculus the principle of differentiation is the hypothetical reduction of increments in inputs and outputs to infinitesimal size. From these considerations, differentials (e.g., dy/dx) can be derived. These differentials are often referred to as rates of change and have particular applications in applied mathematics and physics, where mathematical models are used to simulate actual physical scenarios. So this is important for hydrodynamics, electrodynamics, engineering, mechanics, astronomy, cosmology, etc.