Limits - Race between two variables while some explode and while some vanish.

Limits - Race between two variables while some explode and while some vanish.

Limit is like log and modulo, an algebraic construct. 

Discontinuity has a major impact over limits. For a Limit to exists, the function or variable should be rotating or keep moving. Two Discontinuity exists - 1. Infinite Discontinuity (Asymptotes), 2. Definite Discontinuity - Floor/Ceil function, Manual - IN reality, functions are discontinuous at various points or not defined.

Derivative can be defined only with Limit reducing the difference / gap, to get a particular value of a function. It is a special kind of math with properties.

References:

https://byjus.com/maths/limits-and-derivatives/