北京 景山 学校 数学系
Calculus ++ @ MATHEMATICS @ Senior 2  。2009-2010
jiguanglaoshi@gmail.com

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[2] October
[updated : 09/11/25 ]
Date
 Activities / Objectives
  Images / Home Work
 Remarks / Images
 References / Links
Tuesday

Oct. 13

14:50 -16:20

  • Return Assignment # 1 (parabolas)
  • Collect Assignment # 2 (hyperbolas)
  • Handout Assignment # 3 (derivatives)


  • Use the derivative to prove the theorem about the tangent line to a Parabola in (1/a;1/a)
  • General Definition of a the derivative number.
  • General definition of a DERIVATIVE FUNCTION.
  • Formulas of the elementary derivative functions (Chart).
 d

Equation of the tangent line @ x=a
tang		 tp
 Assignment # 1

Assignment # 2

Assignment # 3

Exercises Derivatives
formulas
Tuesday

Oct. 20

14:50 -17:00
  • Return Assignment # 2 (hyperbolas)
  • Collect Assignment # 3 (derivatives)
  • Handout Assignment # 4 (rational funct.)
  • Definifion of the Maximum and minimum of a function on a given interval.
Theorems of variations related to the derivatives
  • f '(x) > 0 on [a;b] ==> f is increasing on [a;b]
  • f '(x) < 0 on [a;b] ==> f is decreasing on [a;b]
  • f '(x) = 0 on [a;b] ==> f is constant on [a;b]
Examples on the fonctions given in Assignment #3
(graph shown on computer).
f1Gr  f2Gr

f1                  f2
 [Visit of Wu Peng Lao Shi]

M is a Maximum of f on [a;b]
if and only if
max
Assignment # 2

 Assignment # 3

 Assignment # 4
Tuesday

Oct. 26

14:50 -17:00
  • Return Assignment # 3 (derivatives)
  • Collect Assignment # 4 (rational funct.)
  • Handout Assignment # 5 (asymptotes)
Discussion of the general theorems on limits with or with undecided cases (see chart)
Examples with rationnal functions.

Definition and ex. of Asymptotes (straight lines)
  • parallel to (Oy) (x = a)
  • parallel to (Ox) (y = b)
  • oblique (y = ax + b )
Formal definition : (D) y = ax + b is an oblique asymptote to the curve of a function f, if and only if :
das

 Asymptotes
ax  yb
yab


UNDECIDED forms of limits

u

(never write any of these as an actual limit ! )

Note:
because of the mid-term exam,
Tues. Nov. 3 class is cancelled
and Assignment #5 is postponed to Nov.10

General Theorems
on limits
with undecided cases

Assignment # 3

 Assignment # 4

 Assignment # 5