Note: This comprehensive formula sheet covers all major topics in AP Calculus BC.

📚 Table of Contents

1. Limits & Continuity
2. Derivatives
3. Integration
4. Series
5. Parametric/Polar
6. Differential Equations

Limits & Continuity 📊

Special Limits

• $\lim_{x \to 0} \frac{\sin x}{x} = 1$
• $\lim_{x \to 0} \frac{1-\cos x}{x} = 0$
• $\lim_{x \to \infty} (1 + \frac{1}{x})^x = e$

Derivatives 📈

Basic Rules

• Power Rule: $\frac{d}{dx}[x^n] = nx^{n-1}$
• Product Rule: $\frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)$
• Quotient Rule: $\frac{d}{dx}[\frac{f(x)}{g(x)}] = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$
• Chain Rule: $\frac{d}{dx}[f(g(x))] = f'(g(x))g'(x)$

Common Derivatives