AP CALCULUS · MODULE 01

Limits & Continuity
The Foundation of Calculus

Understanding limits is essential for derivatives and integrals. Click on any topic below to explore with detailed examples.

📘 BUders Learning System

This module covers the fundamental concepts of limits and continuity. Study each topic in order for best results.

What is a Limit?

Intuitive definition, notation $\lim_{x \to a} f(x) = L$, understanding from graphs.

definition → start

⬅️➡️ 02

One-Sided Limits

Left-hand limit $\lim_{x \to a^-} f(x)$ and right-hand limit $\lim_{x \to a^+} f(x)$.

two-sided vs one-sided → start

Sum, difference, product, quotient, power, and root laws for limits.

properties → start

Limits at Infinity

$\lim_{x \to \infty} f(x)$ and $\lim_{x \to -\infty} f(x)$, horizontal asymptotes.

end behavior → start

Infinite Limits

$\lim_{x \to a} f(x) = \infty$, vertical asymptotes.

vertical asymptotes → start

Definition of continuity at a point, on an interval, types of discontinuities.

continuous functions → start

Intermediate Value Theorem (IVT)

If $f$ is continuous on $[a,b]$, then $f$ takes every value between $f(a)$ and $f(b)$.

theorem → start

Squeeze Theorem

If $g(x) \le f(x) \le h(x)$ and $\lim g(x) = \lim h(x) = L$, then $\lim f(x) = L$.

sandwich theorem → start

Practice Problems

20 solved problems covering all limit and continuity topics.

practice → start

20-question interactive quiz with instant feedback.

assessment → start