data/knowledge_base/calculus.md

Calculus – Basic Overview

Limits

lim (x → a) f(x)

• Check left-hand and right-hand limits
• Limit exists only if both are equal

Continuity

A function is continuous at x = a if:

1. f(a) exists
2. lim (x → a) f(x) exists
3. lim (x → a) f(x) = f(a)

Applications

• Tangents
• Rate of change
• Optimization

Common Mistakes

• Direct substitution without checking form