data/knowledge_base/limits.md

Limits – Key Rules

Standard Limits

lim (x → 0) sin x / x = 1
lim (x → 0) (1 − cos x) / x² = 1/2

Techniques

• Factorization
• Rationalization
• Standard identities

Infinite Limits

If f(x) → ∞ as x → a, limit diverges

Common Mistakes

• Cancelling terms incorrectly
• Ignoring domain restrictions