COALITION MATH 151, FALL 1997

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

                             Day 15.1


1.  Main techniques for finding vertical and horizontal 
asymptotes.  (Subsumes 2C of previous day.)

INTERRUPTIONS TO COLLECT PROJECT REPORTS AND FILL OUT 
EVALUATIONS.

2.  Team RAT -- Example 3:  f(x) = 2x^2/(x^2 - x - 2).
THIS WAS TOO HARD FOR THEM TO DO WELL IN THE TIME ALLOTTED.  
INSTRUCTIONS WERE TO USE MAPLE ONLY TO SOLVE f"(x) = 0.  IN 
RETROSPECT IT WOULD HAVE BEEN BETTER TO ALLOW MAPLE FOR ALL 
ALGEBRAIC CALCULATIONS BUT FORBID USE OF ANY PLOT COMMAND.

3.  Motivational remarks postponed from an earlier day:
Why study concavity?  (Why eat broccoli?  Motivation presented to 
a child may not be the real reason.)  Challenge:  Prove that if 
f"(x) = (x^2 + 1)f(x) and f(0) = 0, f'(0) not 0, then f(x) is not 
zero for any other value of x. 
I INDICATED BRIEFLY WHY THE THEOREM IS TRUE, AND EMPHASIZED THAT 
STUDENTS SHOULD LEARN TO FOLLOW PROOFS OF SUCH THINGS WITHOUT 
GLAZING OVER, NOT NECESSARILY DISCOVER THEM THEMSELVES.

4.  More examples:  Subtract 10 from your team number and do the 
corresponding problem on p. 224.
NO TIME FOR THIS.