COALITION MATH 151, FALL 1997

        Group II (S. A. Fulling, assisted by Cary Lasher)

                              Day 10.1


    1.  Miscellaneous properties of the definite integral 
    (postponed from last week)

    2.  Individual RAT on fundamental theorem I and integration 
    by substitution.  Give answers.

    3.  Activity:  Grade 3 (concocted) student attempts at a 
    definite integral by substitution.  (Point out that 
    transforming the limits is a valid alternative to back-
    substitution, but not handling limits properly is wrong.)

    4.  Something left over from earlier (see ms. submitted to 
    Math. Mag.):  Vectors vs. related rates.

        A.  Problem of 2 cars leaving point at same time in 
        perpendicular directions.  Rate of separation calculated 
        as norm of relative velocity; anything wrong with that?

        B.  Problem of 2 cars approaching point but not arriving 
        at same time.  Vector calculation and standard 
        calculation give different, but almost equal, answers.
        Prize questions:

           i.  Why are the answers different?

          ii.  Why are they so close?
BARELY HAD TIME TO STATE THE PROBLEM -- DISCUSSION POSTPONED.