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Calculus

Limits and continuity

Calculus

Cover of Math Bytes Calculus episode 1: Limits from a graph

Calculus · EP1

Limits from a graph

A limit is the y-value a graph is heading toward as x gets close to a number, not the value the function actually has there. If f(x) = x + 2 has a hole at x = 2, the limit as x approaches 2 is still 4.

Cover of Math Bytes Calculus episode 2: Continuity

Calculus · EP2

Continuity

A function is continuous at x = a when three checks pass: f(a) exists, the limit as x approaches a exists, and the two are equal. A jump in the graph breaks the second check.