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2.1 Informal Definition of Limit and Continuity

2.1.1 Limits

A function has a limit at x0 if whenever x is near x0 and x not equal to x0, f(x) is near h.

This is written


2.1.2 Continuity

A function f is continuous at x0  if whenever x is near x0, f is near f(x0).

A continuous function has no "gaps". Proof


2.1.3 Limits and Continuity

Continuity of f at x0 means that