Special and piecewise functions
Piecewise, step, floor and other functions you meet in limits and continuity.
Piecewise functions
f(x) = \begin{cases} f_1(x) & x < a \\ f_2(x) & x \ge a \end{cases}
Piecewise functions explained: how to read and graph them, find one-sided limits, check continuity and differentiability, and integrate across pieces.
Floor and ceiling functions
\lfloor x \rfloor = \max\{n \in \mathbb{Z} : n \le x\}, \quad \lceil x \rceil = \min\{n \in \mathbb{Z} : n \ge x\}
The floor function ⌊x⌋ and ceiling function ⌈x⌉: definitions, step graphs, one-sided limits, continuity, derivative and how to integrate them.
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