Week 7 = finish 8.1 (seq), 8.2(ser)

Activities: harel's got lots.  html versions are in the activities
directory.

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M - more 8.1

Talk indeterminate forms of limits: use algebra or L'hospital's rule
 to solve these (10-15 min)
   (0/0, (+-)inf/(+-)inf,  0*(+-)inf, inf-inf,  0^0, inf^0, 1^inf )

Go over activity (10 min)
  difference between a sequence and a function 
     (introduce, but don't solve:
       example 7-- a_n = n!/(n^n), doesn't make sense to them to 
       talk about a continuous function f(x)=x!/(x^x)  )
  how to find limit of sequence using limit of a function
  draw picture showing div. of function doesn't imply div. of sequence
     (f(x) = cos(2 pi x)    a_n=f(n)=1

introduce comparison test/squeeze thm. (15 min)
  work example on board: (show sin(n)/n converges)
  solve earlier example n!/n^n

introduce bounded monotone seq, -defn/thm. (10 min)

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T - 8.1/8.2

8.1:
Activity: How do your favorite sequences stack up? (20 min)

discuss recursively defined seq. and induction (25 min)
  work example (sqrt activity) on board 

8.2:
start? to define series as limit of partial sums and
define convergence and divergence of series (5 min)

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W - 8.2

define series as limit of partial sums and
define convergence and divergence of series (15 min)

examples:
  geometric series (10 min)

Activity: Series, Integrals, and Hidden Patterns (25 min)

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R/F - 8.3

review def of conv/div (5 min)

examples continued: 
  telescoping (5 min)
  harmonic series (prove divergence!!!) (10 min)

nth term test for divergence ("are you paying attenion test")  (5 min)

series laws (sums, constant multiple) (10 min)
  include how this relates to conv/div
  do couple of simple examples

More examples (5-10 min)
  (examples avail. in group activities of Stewart)


ASSIGN PROJECT #2 (5-10 min to find groups!)

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