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For more information, please see full course syllabus of College Calculus: Level I
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Lecture Comments (8)

0 answers

Post by Huseyin Kayahan on February 14, 2013

Calculations.. calculations... just put initial state of the problem, give the answer directly and let people do the calculations on their own.
And with the time saved here, put emphasis on "reasons", why do i need this, why is that, why that slope, a real world example of making use of this. People are here because they seek for something different in terms of teaching, but what I see here is exactly the same as I see in my regular college courses which I avoid attending.

0 answers

Post by Donald Bada on January 21, 2013

e is a pre-determined mathematical constant. Formally known as Euler's number the number e is approximately equivalent to 2.71828 which is the base of the "natural" logarithm and it is the limit of (1+1/n)^n as "n" approaches infinity... I hope this helps, somewhat.

2 answers

Last reply by: Dave Seale
Fri Aug 16, 2013 6:49 AM

Post by Laurine Laidlaw on July 21, 2012

I had the same question. WHERE DOES E COME FROM?

0 answers

Post by Gerard Howard on April 29, 2012

where did the value of e come from? I get the rest but not knowing where the value of e came from just throws the whole lesson out of perspective for me.

Average and Instantaneous Rates of Change

  • Start by sketching the function, and sketch the required secant lines or tangent lines.
  • The average rate of change is a secant line slope.
  • The instantaneous rate of change is a tangent line slope.
  • Instantaneous rates of change can be found by either taking a limit of average rates of change or by computing a derivative directly.

Average and Instantaneous Rates of Change

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Rates of Change 0:11
    • Average Rate of Change
    • Instantaneous Rate of Change
    • Slope of the Secant Line
    • Slope of the Tangent Line
  • Lecture Example 1 1:14
  • Lecture Example 2 6:36
  • Lecture Example 3 11:30
  • Additional Example 4
  • Additional Example 5