COALITION MATH 152, SPRING 1998

              (S. A. Fulling, assisted by Vera Rice)

                             Day 19.T


    1.  The usual paper shuffling:  Old homework, CAPA, revised 
    new homework, lab sheet if ready.

    2.  Call on a team to present the proof of the integral 
    formula involving arcsin (see last time).  Finish the 
    discussion of inverse trig functions from last time.
SEE NOTES ON DAY 18.R:  TEAM PRESENTATION WAS CANCELLED, THE REST 
WAS TRUNCATED AND RUSHED.  THE DETAILS OF INVERSE TRIG SHOULD BE 
RELEGATED TO A WEB PAGE.
     
    3.  Congratulate teams on their max-min solutions on the Web.
TWO SOLUTIONS ARE STILL NOT QUITE SATISFACTORY, ONE FOR 
SUBSTANTIVE AND ONE FOR TECHNICAL REASONS.

    4.  L'Hospital's rule (following web page)

        A.  A good example:  lim_{x->0} (1 - cos(3x))/x^2.  (Show 
        that this can also be done by quadratic approximation.) 

        B.  A bad example:  lim_{x->\pi} (1 - cos(3x))/x^2

        C.  0 times infinity:  Write as a quotient in the right 
        way.

        D.  Implications for asymptotics of exp and ln.

        E.  Infinity - infinity:  Try to put over a common 
        denominator and use L'Hopital.

        F.  0^0, infinity^0, 1^infinity:  Take log, then apply 
        L'Hopital.  Remember to exponentiate at the end!  (What 
        IS 0^0 anyway?)  

        G.  A quiz.  (Provide answers.)
QUIZ INCLUDED ONE PROBLEM TO WHICH L'HOPITAL IS INAPPLICABLE, ONE 
OF AN a^b TYPE, AND THE INVERSE FUNCTION DERIVATIVE POSTPONED 
FROM LAST TIME.

    5.  Preparation for the next lab

        A.  Option One:  Hard max-min problems with Maple help.

        B.  Option Two:  Why are leading digits of data 
        logarithmically distributed?  Also discuss slide rule and 
        its relation to logarithmic graph paper.
THIS NEEDS TO BE BETTER PRESENTED.  OVERALL, THIS DAY WAS 
EXTREMELY RUSHED, AND MY PREPARATION FOR POINT 5 WAS INADEQUATE.