北京 景山学校 数学系
Calculus ++ @ MATHEMATICS @ Senior 2.4  。2010
jiguanglaoshi@gmail.com

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[2] October
[updated : 2010/10/19]
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Tuesday

Oct. 12

15:15 - 16:45

 Chapter II
 Formal definitions of  some limits :
Lim_def
 
 Examples and illustration
  1. lim_hom1                Asymptote : y = 2

  2. lim_hom2
                  Asymptote : x = 1

  3. lh3
Assignment # 3 to be prepared for Oct.19
 fig
  1. For any e > 0, there is an A > 0,such that x > A ==>  b < f(x) < b+e

  2. For any A > 0,there is an e > 0,such that a < x < a+e ==>   f(x) > A 

  3. For any e > 0,there is an A > 0, so
    a-A<x<a+A     ==>  b-e < f(x) < b+e

  4. For any A> 0, there is a B > 0, such that x > B ==>  f(x) > A

Tuesday

Oct. 19

14:25 - 16:05
General theorems on limits :
  • Study of the chart of Limits of the SUM, PRODUCT, QUOTIENT of two functions.

  • Study of the typical UNDECIDED CASES :
                            未确定
            ∞ - ∞   ;  0 x ∞  ;  ∞ / ∞

  • Examples of use of these theorems :
    see next columns.

  • Chart of the Infinite branches
Application of the theorems to the limit of polynomials and rationnal fractions when x -> ∞

lim_pol

frac
cases
Examples :

pol

frac_rat


Tuesday Oct. 26
纪光老师在成都
上课跟吴鹏老师

Chart of Limits_SPQR

Answers / Chart of Limits SPQR

Assignment # 3
to be completed and retrurned for
Friday Oct. 22.

Assignment # 4
To be handed out by
吴鹏老师
on Tuesday Oct.26