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Chapter 2: Limits and Derivatives

Visual Calculus / Limits and Continuity
An excellent site that has tutorials covering virtually everything about limits, continuity, and asymptotes. Limits are presented numerically, graphically, and symbolically. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.

Section 2.1: The Tangent and Velocity Problems

Animated Secant Approaching the Tangent
A Java applet animation that shows a secant approaching the tangent line.

Section 2.4: The Precise Definition of a Limit

Definition of Limit
A presentation of the definition of limit, along with a number of solved examples.

Section 2.5: Continuity

Continuity and Discontinuity
Definitions and examples of continuity and discontinuity both at single points and on intervals.

Section 2.6: Limits at Infinity; Horizontal Asymptotes

Limits of Functions as x Approaches Infinity
Practice questions provided by UC Davis, with solutions.

Section 2.7: Tangents, Velocities, and Other Rates of Change

Tangent Line as the Limit of Secant Lines
Construction of the tangent line as the limit of secant lines at a point.

Rate of Change Applied to Import/Export
Discussion of rates of change with an example using export data

Visual Calculus / Derivatives
An excellent site that has tutorials covering virtually everything about derivatives. It also has interactive online applets, practice problems with solutions, examples, quizzes, and tutorials on using graphing calculators.

Section 2.8: Derivatives

Derivatives Using the Limit Definition
This is a set of practice problems about derivatives provided by the University of California, Davis, with solutions.

Section 2.9: The Derivative as a Function

Derivative as a Function
A thorough examination of the concept of the derivative as a function. This site includes a number of worked out examples and is intended to be used with a CAS.