The core concept in Calculus (Main).

Transclude of Limits-Notation

Say, . On first glance, could just be , but really, is undefined.

This means that there must be a restraint, a limit, which is written as .

This would be graphed as

Transclude of YAAAA

SO: would be equal to whatever number that y-axis is closest to.


This is the second example, basically the given is

which basically means that follows a parabolic curve—specifically, —up until , when it breaks that pattern and becomes . So when asked the value of , it is simply asking to what value is reaching as goes closer and closer to ? The answer is four, which could be answered visually—by plotting the graph—or by solving the functions of while is going closer and closer to the limit .


Epsilon-Delta Definition of Limits