COALITION MATH 152, SPRING 1998

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

                             Day 27.T


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

    2.  INDIVIDUAL RAT:  State the epsilon-delta definition of
    lim_{x->2} (3x - 1) = 5  and prove from the definition that 
    the statement is true.
PRETTY MUCH A WIPEOUT ...

    3.  TEAM ACTIVITY:  Put a group consensus answer to the RAT 
    on plastic.
SUCCEEDED IN ELICITING SEVERAL DECENT RESPONSES.

    4.  Four ways of finding the Maclaurin series of 1/(5 - 3x)
    (postponed from a week earlier).
STUDENTS CAME UP WITH TAYLOR'S FORMULA AND GEOMETRIC SERIES 
METHODS.

    5.  Limits at infinity and infinite limits

        A.  Introduction

            i.  What they mean geometrically:  Horizontal and 
            vertical asymptotes

           ii.  What they REALLY mean:  epsilon-delta-type 
            definitions.

          iii.  How to evaluate or recognize them (in the 
            simplest cases):

                a.  Horizontal:  Divide numerator and denominator 
                by the highest power appearing in the 
                denominator.

                b.  Vertical:  Look for places where the 
                denominator is zero.

        B.  Some examples (going beyond the simplest rational 
        functions) with student assistance
MY RECORDS AND MEMORY ARE INADEQUATE HERE.