Video Notes on Limits and Continuity

Vocabulary flashcards covering limits, continuity, and basic function behavior as discussed in the video notes.

Continuity of sine and cosine

Sine and cosine are continuous everywhere; you can draw them without lifting a pencil.

Domain of sqrt(x+13)

Defined for x ≥ -13; the function is continuous on its domain.

Vertical asymptote at x = -2 for f(x) = 1/(x+2)

As x approaches -2 from the left, f(x) → -∞; from the right, f(x) → +∞; the limit does not exist.

Removable discontinuity (hole)

A hole in the graph where the limit exists and the hole could be filled to make the function continuous.

Open circle vs closed dot

An open circle indicates a point not included; a closed dot indicates the point is included/defined.

Polynomial vs rational function continuity

Polynomials are continuous everywhere; rational functions are continuous wherever the denominator is nonzero.

Monotonicity of f(x)=1/(x+2)

Derivative f′(x) = -1/(x+2)^2 < 0 for all x ≠ -2; the function is decreasing on (-∞, -2) and (-2, ∞).