The theory of limits and continuous functions usually appear in a calculus text with graphical and numerical interpretations.

Here are some of the most common results that are frequently discussed and used in a calculus course.

CCD.UCL Uniqueness and Calculus of Limits.

CCD.BMF Bounded and Monotonic Functions

Function Limits and Sequences

Continuity Calculus

CCD.IVT The Intermediate Value Theorem

The Intermediate Value Theorem and The Bisection Method

CCD.EVT The Extreme Value Theorem

Definition of Continuity (at a point):