北京 景山学校 数学系
Calculus ++ @ MATHEMATICS @ Senior 2.4  。2011-12
jiguanglaoshi@gmail.com

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[2] November
[updated : 2011/11/30]
Date
 Activities / Objectives
  Images / Home work / Assignments
 Remarks / Images
 References / Links

Thursday

Nov. 3

4:05 - 4:45
  • Return of Assignment # 4 / Limits
  • Corrections on Assignment # 3
  • OBLIQUE ASYMPTOTES :
                  ( x -->∞  & y -->∞)
    • Asymptotic directions :
      • parabolic type / Oy :
        • Lim f(x)/x = ∞
      • parabolic type / Ox
        • Lim f(x)/x = 0
    • Lim f(x)/x =a
    • Lim [f(x) - ax ] = b
    • Lim [f(x) - (ax+b)] = 0
    • Lim [f(x) - g(x)] = 0
    • Position / Asymptote
Dir_Par_Oy_fig.png    Dir_Par_Oy.png

Dir_Par_Ox_fig.png

Dir_Par_Ox.png
Frac_rat_asympt.jpg

Asympt_eq.jpg

Frat_Obl_Asympt.png




Assignment #2
Exercises on Limit
1-10


Assignment #3
Exercises on Limit
11-20

MEMO / ASYMPOTES

Friday

Nov. 4

4:05 - 4:45
Thursday
Nov. 10
Friday
Nov. 11
期中考试 - Midterm Exam -期中考试 - Midterm Exam - 期中考试 - Midterm Exam -
期中考试 - Midterm Exam - 期中考试 - Midterm Exam - 期中考试 - Midterm Exam











Thursday

Nov. 17

4:05 - 4:45
Friday

Nov. 18

4:05 - 4:45
  • Introduction to the DERIVATIVE :
    • Introduction : computer animated demo :
      in search of the limit of the rate of growth
      • tangent to a Parabola
      • tangent to Hyperbola
    • Formal definition 
    • Tangent line equation
  • EXERCISES of calculations of derivatives :
  • in one point
  • in a current point
  • Def. of the DERIVATIVE FUNCTION :
  • Direct calculation of the derivative function examples :
  • trinomial
  • homographic
  • Radical : 1/√
  • Under-Tangent to a Parabola :
    => proper construction.

  • FORMULAS of the derivatives :
    • Elementary functions (Chart I)
    • Sum / Product / Quotient / Radical (Chart II)
    S2_Tangent_Parabola.jpg

    def_d(a).jpg
    this limit, noted  f '(a) , is the limit of the slope of the secant line to the curve from A(a; f(a)).
    By definition it's the slope of the tangent line to the curve of  f  in this point A(a; f(a))
    Equ. of the tangent line :
    Equ_tangente.jpg

    Demi_parab_sous_tan.png

    Calc_Df(x).png

    f '(0) = 1/2
    f '(2) = -1/2


    Assignment #4
    Def. of the Derivatives




    MEMO / Exercices
    [Assignment # 5]
    Chart I & II
    Derivatives of
    Elementary functions
    Derivatives of
    SPQR
    Thursday

    Nov. 24

    4:05 - 4:45
    • Correction of the exercises of Ass. #5
      (Use of the formulae of the derivatives)
    • Short Test on these formulae.
    • Applications of the Derivatives :
      • Theorem of variations
      • Determination of Extrema
      • Chart of the variations and limits
      • Graph with asymptotes & Tangent.



    Assignment #4
    (p.2/2)
     Applications
    of the Derivatives
    Friday

    Nov. 25

    4:05 - 4:45
    • Return marked Tests with Answers

    • Applications of the Derivatives :
      • Theorem of variations :
        • f '(x) > 0 <=> f increasing
        • f '(x) < 0 <=> f decreasing

      • Determination of Extrema

      • Chart of the variations and limits

      • Graph with asymptotes & Tangent
    • Exercises : in class + Ass. # 4 p.2
    • Exercises to prepare for Thursday Dec. 02
    • Definition of Maximum and Minimum is relative to a given interval.

    • The Zeroes of the derivative do not necessarily correspond to a Max or a Min of the function : watch the change of sign !

    • The position of the curve / Asymptotes can be determined by the variations instead of a special study of the signs.


    Senior_2.4_2011-12_Ass_4_p.2_graph.png

    TEST on DERIVATIVES
    ANSWERS

    Assignment #4
    ANSWERS
    (p.2/2)
    Applications
    of the Derivatives

    Assignment #6
    Study and Graph
    of rationnal functions