Chapter 01
LIMITS
The foundation of all Calculus. Before we can measure change or accumulation, we must understand the behavior of the infinitely close.
01
The Precise Definition
The Game of Proofs
Master the formal "Hitbox Game" that defines calculus. Prove limits exist by trapping the function.
02
Limit Laws
Algebraic Toolbox
Stop guessing numbers. Learn the algebraic shortcuts to solve 0/0 problems analytically.
03
Infinite Limits
Vertical Asymptotes
What happens when x explodes? Explore behavior near asymptotes and the concept of growth.
04
Continuity
The Unbroken Path
Define smoothness mathematically. Fixing broken functions and the Intermediate Value Theorem.
05
L'Hôpital's Rule
The Derivative Hack
The ultimate shortcut for indeterminate forms. Using derivatives to solve impossible limits.