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

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[3] November
[updated : 2010/12/23]
Date
 Activities / Objectives
  Images / Home work / Assignments
 Remarks / Images
 References / Links



Tuesday


Nov. 02

14:25 - 16:05
  • Return of Assignment # 4 / Limits
  • Corrections on Assignment # 3 & # 4

  • 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
  • Examples
  • Exercises / Assign. #3 & #4
FR

frat as
as








Assignment # 5
Oblique Asymptotes

Tuesday

Nov. 09

14:25 - 16:05
  • 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 :
      f '(a)
      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))
    • Tangent line equation :
      tan
  • EXERCISES of calculations of derivatives :
  • in one point
  • in a current point
  • Def. of the DERIVATIVE FUNCTION :
  • calculation of the derivative function
  •  trinomial
  • homographic

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

    st



    sec_tan






    Assignment # 6
    Derivatives





    Tuesday

    Nov. 16

    14:25 - 16:
    • Return Ass. #6 + Answers / comments
  • Short Test on formulas

    •
  • Variations of functions :
  • increasing / decreasing / [a ; b]
  • Maximum & Minimum / [a ; b]
  • Theorems / Derivatives :
  • f '(x) > 0 ==> f  incr. / [a ; b]
  • f '(x) < 0 ==> f  decr. / [a ; b]
  • Chart of variations and limits

    • •  Graph : asymptotes + tangent + curve






    ANSWERS :  TEST
    Formulas of the Derivatives


    Assignment # 7
    (derivatives, variations & graphs)








    Tuesday

    Nov. 23

    14:25 - 16:05
    Return & Correction of the first 6 functions
    on Ass.#7
    Review :
  • Variations of functions :
  • increasing / decreasing / [a ; b]
  • Maximum & Minimum / [a ; b]
  • Theorems / Derivatives :
  • f '(x) > 0 ==> f  incr. / [a ; b]
  • f '(x) < 0 ==> f  decr. / [a ; b]
  • Chart of variations and limits
  • Graph :
  • asymptotes
  • tangent
  • curve

    • • Singular points of curve :
    • Inflection points :
      • definition
      • determination
    • Cusp points :
      • Left and right derivatives
      • "vertical" tangents
      • angular points
    Test
    General study of a function
    TAf
    Singular points

    cusp1           Inflex_vert
    Niao   VerInflex

    Cusp2

    PtAng

    TAf

    TA



    Study of CUSPS
    In each point where the derivative cannot be defined by the usual formulas, find the limits of the growth rate on the right and on the left sides of the point :

    Right derivative
    RD

    Left derivative
    LD
    f is not derivable in a if ß ≠ alpha
    (two half tangents : angular point)

    VD
    Vertical half tangent

    Test has been returned
    by 吴老师
    on Thursday 24th




    Test A
    Test B
    General study of a function


    Test A&B SOLUTIONS


    Assignment #8
    singular points :
    inflection
    cusps
    Tuesday

    Nov. 30

    15:15 - 16:55
    • Return of Assignment # 8
    • Corrections :
      • Derivatives aboslute value
      • Cusps
      • Asymptotes
    • Introduction to the concept of :
      Continuty / Discontinuity
      of a function @ one point :
      • definition
      • examples :
    d1f          D2f

    D3f
    d1   D2fig

    D3fig
    Too many students copy wrong calculations on each other, or don't do the homework.
    A  few students think that
    "it's useless to do the homework " !
    吴老师
    took the class to tell them that
    it was not right     !


    Next and last
    TEST
    December 14th
    Review of the whole semester
    Complete study of a function
    Correction of Assignment # 8 will be on line by December 6th.

    cf.     Next month  ==>