Level Curve: level curve at z=c is the curve in R^2 of z = f(x, y).

Contor Map: several labeled level curves on same coordinate axes (ie. multiple level curves in the same direction)

Vertical Trace: making one independent (instead of dependent) variable constant

Functions with Three Variables

Functions with Three Variables: w = f(x, y, z)

a hypersurface in \mathbb{R}^4

visualize by Level Surfaces

If z = f(x, y), the limit of f(x, y) as (x, y) approaches (a, b) is C, denoted \lim_{(x, y) \rightarrow (a, b)} f(x, y) = C provided that for all \epsilon so that when 0 < \text{dist}((x, y), (a, b)) < S, |f(x, y) - C| < S