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For more information, please see full course syllabus of College Calculus: Level I
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Lecture Comments (4)

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Post by Jason Mannion on November 14, 2011

how do we evaluate a table of x, and f(x) without being given the function, using the midpoint rule?
Eg. when x=2, f(x)=4. when x= 5/2, f(x) = 9, etc etc. say we have this table, and we are to evaluate it from 2 to 5. deltaX = 1/2. midpoints are 2.25,2.75,3.25,3.75,4.25,4.75... I don't know what f(x) at these points are. Should I just make a graph and estimate it?

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Post by Senghuot Lim on September 26, 2011

u love u prof. Switkes

1 answer

Last reply by: andy newton
Mon Nov 18, 2013 4:36 PM

Post by nerway ray on April 23, 2011

how do you know where to start on the sketch of the graph once you draw.

Approximating Areas and Distances

  • I recommend starting with a sketch of the function.
  • Determine the correct width for the approximating rectangles.
  • Draw in the first couple, and last, approximating rectangles.
  • Be careful to include the correct function evaluation for each height.

Approximating Areas and Distances

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
  • Three Approximations 0:12
    • Right Endpoint, Left Endpoint, Midpoint
    • Formulas
    • Velocity and Distance
  • Lecture Example 1 2:28
  • Lecture Example 2 12:10
  • Lecture Example 3 19:43
  • Additional Example 4
  • Additional Example 5