Introduction to Continuity for Calculus

This video introduces the idea of discontinuity in calculus. First, we use an intuitive idea of continuity: if a function can be drawn without picking up your pen or pencil, it is continuous. For a more mathematical definition of continuity, we use the calculus definition, which is summarized in the continuity checklist. For a function to be continuous at x=a, three conditions must be fulfilled:

1. The function must be defined at x=a (a must be in the domain of f)
2. The limit must exist at x=a
3. The limit must equal f(a), that is, the value of f evaluated at a

The video then gives an example of a function with multiple discontinuities and asks us to describe why the function is continuous at each discontinuity.

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