Calculus Lecture Notes: Limits, Continuity, Derivatives, Integrals, and Series (Vocabulary Flashcards)

A set of vocabulary flashcards covering the core concepts from the provided notes.

Limit

The value that f(x) approaches as x approaches a. A limit exists when the left-hand and right-hand limits exist and are equal.

Left-hand limit

The limit of f(x) as x approaches a from the left (x → a⁻).

Right-hand limit

The limit of f(x) as x approaches a from the right (x → a⁺).

Squeeze theorem

If f(x) ≤ g(x) ≤ h(x) near a and lim f = lim h = L, then lim g = L.

Indeterminate form

A limit form (e.g., 0/0 or ∞/∞) that requires algebra to evaluate.

Continuity

A function is continuous at a if lim_{x→a} f(x) = f(a); no holes, jumps, or breaks at a.

Removable discontinuity

A discontinuity where the limit exists but f(a) ≠ limit; can be