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AP Calculus - Continuity, Rate of Change of functions and Tangents

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Contents of this course

When is a functions continuous?

Identifying a continuous function from graphs (5:50)
Rigorous definition of continuity (12:12)
Removable discontinuity (18:55)
When is a function continuous in an interval? (8:51)
Properties of continuous functions (5:30)
Intermediate Value Theorem (9:07)

Tangent to a curve at a given point and its slope

Tangent as the limiting case of a secant (25:57)
How to find the slope of the tangent (26:06)
Equation of the tangent and normal to a curve at a given point (7:38)
Horizontal and Vertical Tangents (10:01)

Average Rate of Change

Conceptual Meaning (4:13)
Mathematical definition and its relation to the slope of the secant (4:05)

Does the tangent always exist?

When does a tangent exist or not exist (2:49)
Example 1 - Does the tangent exist for abs(x) at x=0? (3:48)
Example 2 - Does the tangent exist for a step function at x=0?
Example 3 - Another piecewise function for which the tangent does not exist (21:26)

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