Sep 22

Here are two problems I used in my calculus 1 class, just after teaching them the definition of the derivative and discussing average and instantaneous rates of change.

 

  1. My car has a digital read out with the average fuel economy.  I used to have a car which also had the instantaneous fuel economy.
    AverageFuelEconomy
    What is the difference between these two fuel economies?  Under what circumstances is each more useful?  How can I use the average fuel economy feature to approximate my instantaneous fuel economy?  (Your answer should be  2-5 complete sentences).
  2. Read the article at
    http://www.slate.com/blogs/bad_astronomy/2015/09/03/ice_loss_greenland_and_antarctica_lost_5_trillion_tons_since_1992.html .
    You can use this QR code to access it
    QR-code-ice-melt

    1. What is the average rate of change of the mass of Antarctica’s ice?
    2. What is the average rate of change of the mass of Greenland’s ice?
    3. Looking at the graphs, do you think it is reasonable to talk about the instantaneous rate of change for these quantities?  Why or why not?
      Then answer the following questions. Give all answers in complete sentences with units.

 

Apr 13

The FoxTrot Strip from November 6, 2005 contained a “numerical word search”

You can find the strip here.

There are seven clues which are arithmetic problems, but there is also the derivative of 43981 x , the definite integral of x^3 from 0 to 16, and the sum from k equals 0 to 47 of k squared.    I asked my calculus students to perform all these calculations.

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