Review For Test 1 - Limits (VOCABULARY)

Vocabulary flashcards covering definitions of limits, continuity, discontinuities, and key theorems from the notes on pages 1–2.

Limit

The value L that f(x) approaches as x approaches c, if it exists (notation: lim_{x→c} f(x) = L).

One-Sided Limit

Limit of f(x) as x approaches c from one side: left (lim{x→c-} f(x)) or right (lim{x→c+} f(x)); if both exist and are equal, the two-sided limit exists.

Continuity

A function f is continuous at c if lim_{x→c} f(x) = f(c) and f(c) is defined.

Discontinuity

A point where a function is not continuous; the limit may not exist or may not equal f(c).

Removable Discontinuity

Limit as x→c exists and equals L, but f(c) ≠ L or f(c) is undefined.

Jump Discontinuity

Left-hand and right-hand limits exist but are not equal; the function 'jumps' at c.

Infinite Discontinuity

Limit as x→c diverges to ±∞; the function grows without bound near c.

Limit Involving Infinity

Behavior of f(x) as x → ±∞; used to describe horizontal asymptotes; e.g., lim_{x→∞} f(x) = L.

Extreme Value Theorem

If f is continuous on a closed interval [a,b], then f attains a maximum and a minimum on [a,b].

Intermediate Value Theorem

If f is continuous on [a,b], then for every value y between f(a) and f(b) there exists c in (a,b) with f(c) = y.

Piecewise Function

A function defined by different expressions on different intervals of its domain; may be discontinuous at the boundaries between pieces.

Domain

The set of all x-values for which f is defined.

Range

The set of all possible output values f(x) as x varies over its domain.

Continuous Function

A function that is continuous at every point in its domain.

Square Root Function

The function y = √x, defined for x ≥ 0; continuous on its domain [0, ∞).