Flashcards: Understanding Limits and Continuity — 10 cards

Limit — definition?

Value function approaches as x approaches a.

Limit of a function — definition?

Value function approaches as x → a.

Formal ε-δ Limit — role?

Provides rigorous limit definition via ε-δ criteria.

Epsilon-Delta (ε-δ) — purpose?

Formalizes limit rigorously with ε, δ.

Limit Evaluation Techniques — purpose?

Methods like substitution, factoring, L'Hôpital to find limits.

Finite limit — describe?

Limit approaches a specific real number.

Limit at infinity — meaning?

Behavior of f(x) as x → ∞ or -∞.

One-sided limits — left vs right?

Limits approaching from a specific side.

Continuity at a point — conditions?

Function is defined, limit exists, equals function value.

Discontinuities — types?

Removable, jump, infinite.