Section Summary: 2.1

1. Definitions
   • tangent - from the latin, tangens (touching). The tangent line is a line that just touches a curve at a point.
   • secant line - a line passing through two points along the arc of a curve.
   • limit notation - in this section, the notation

     

     means that point Q of the graph will tend toward P of the graph, and as it does the slope will tend toward a value which represents the slope of the tangent line to the curve at point P.

   • Galileo's law - a law of a falling body which we will encounter often in this course, represented here as

     

     This says that the distance that the body falls grows quadratically.

   • average velocity - calculated as the ratio

     

   • instantaneous velocity - the limit of the average velocity as the time elapsed tends to zero.

2. Theorems

   There were no theorems in this section.

3. Properties/Tricks/Hints/Etc.

   Nothing that I noticed.

4. Summary

   Here we focus on the concept of the tangent line, and see how it is either approximated or calculated exactly as a limit of a series of secant lines. The slope of the line may have a physical meaning, such as an average or instantaneous velocity.

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