Reimann Boxes: Fantastic Mathematics Presented Dynamically w/Sketch Pad


Abstract

    The math is not new to you. You've admired it for years. But Sketch pad REALLY permits one to examine the mechanics, results, and beauty. Before boxes, examine tangents, the difference quotient, and the definition of derivative. Then examine intervals, partitions, LEFT, RIGHT, and MIDPOINT boxes, then sums to obtain definite intergal approximations. Then,consider support/note-taking materials and end with the plotting of running sums to polka-dot the graph of the antiderivative.


The Talk

sketchpad sketchpad
Reimann Boxes
  • limit by dragging x, by epsilon-delta, by examining f(x) above and below x, the slope of the secant, and at negative or positive infinity
  • limh4Dx   -- Really shows the derivative is the limit of the direrence quotient. Use this one!!
  • ReimannSums.gsp -- n=8 and 32 LEFT, RIGHT, MIDPOINT slide [a,b] and set [a,b]
  • ReimannSumNotes.pdf -- for taking notes in class and 4 questions (graphics included)
  • ReimannSumANSWERS.pdf -- answers only to student notes/questions
  • e2xSums -- The Antiderivative of ex


In Context

[this semester's schedule w/links] calc1

Support & Origin




[MC,i. Home] calc1 spread sheet notes [Words] Classes [this semester's schedule w/links] [Good Stuff -- free & valuable resources]
© 2019, Agnes Azzolino
www.mathnstuff.com/papers/matycnj19.htm