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Mathematics Dictionary
Dr. K. G. Shih
Diagrams in Calculus
Subjects

  • CA 21 00 | - How to use this program ?
  • CA 21 01 | - Limit and summation
  • CA 21 02 | - Derivative changes the curve of function
  • CA 21 03 | - Sketch using derivative
  • CA 21 04 | -
  • CA 21 05 | -
  • CA 21 06 | -
  • CA 21 07 | - Parametric equations
  • CA 21 08 | -
  • CA 21 09 | -
  • CA 21 10 | - Graphs of R = a + b*F(p*A/q)^M
  • CA 21 11 | -
  • CA 21 12 | -
  • CA 21 20 | -
  • CA 21 21 | -
    • Answers


    CA 21 01. Limit and summary

    • Graphic Method | Calculus
    • 01 01 Limit
      • Start Graphic method
      • Click Menu
      • Click Section 01 in upper box
      • Click Program 01 in lower box. We see the first angle.
      • To see others, Click replot or press Enter key on keyboard
      • Home work : Give the definitions of the 8 angle names.

    Go to Begin

    CA 21 02. Derivative changes the curve of a function

    Diagram Program
    • Diagram | Derivative chages curve.
    • Examples
      • y = sin(x) and y' = cos(x)
      • y = sinh(x) and y' = cosh(x)
      • Parabola is changed to line

    Go to Begin

    CA 21 03.

    Diagram Program
    • Diagram | Sketch using derivative
    • Examples
      • 03 01 : y = 1/(1 + x^2)
      • 03 02 : y = (x - 1)/(x + 1)
      • 03 03 : y = (x^2 - 1)/(x^2 + 1)
      • 03 04 : y = (x^3 - 1)/(x^3 + 1)
    • Reference : See section 3 of Graphic Calculator (GC)

    Go to Begin

    CA 21 04.

    Diagram Program
    Go to Begin

    CA 21 05.

    Diagram Program
    Go to Begin

    CA 21 06.

    Diagram Program
    Go to Begin

    CA 21 07. Parametric equations

    Diagram Program
    • Diagram | Section 7.
    • Diagram 07 01 : x=sec(t) and y=tan(t). From diagram find the signs
    • Diagram 07 02 : x=tan(t) and y=sec(t). From diagram find the signs

    Method : after 1s quadrant, click Re-plot to see next quadrant
    • The signs of y' and y" in 1st quadrant
    • The signs of y' and y" in 2nd quadrant
    • The signs of y' and y" in 3rd quadrant
    • The signs of y' and y" in 4th quadrant

    Go to Begin

    CA 21 08. Conics : hyperbola

    Diagram Program
    Go to Begin

    CA 21 09.

    Diagram Program
    Go to Begin

    CA 21 10.

    Diagram Program
    • Diagram | Section 10 : R = a + b*F(p*A/q)^M
    • Subjects
      • 10 01 : R = a + b*sin(p*A/q)^M
      • 10 02 : R = a + b*cos(p*A/q)^M
      • 10 03 : R = a + b*tan(p*A/q)^M
    • Example : Sketch R = sin(5*A/2)^1
      • Start the program (No download)
      • Click Menu
      • Click section 10
      • Click 01 in upper box
      • Click 01 in lower box
      • Give data 0,1,5,2,1 (a=0, b=1, p=5, q=2 and M=1)
      • Change scale ?
      • Click 2 in left side box (R window = 2)
      • Click re-plot

    Go to Begin

    CA 21 11.

    Diagram Program
    Go to Begin

    CA 21 00. How to use sketch program

    Diagram Program
    • Diagram | How to use ?
    • 1. Start sketch program
      • Clcik Diagram program above
      • Select run at current location
      • Select yes to run
    • 2. Run program 07 01
      • Click Menu command
      • Click polynomial function in section 07 in upper box
      • Click Program 01 in lowe box
      • It has 4 steps. After 1st step, click Re-plot
    • 3. What is demo command ?
      • Click Menu then click Demo
      • Select a section number
      • Slect a program
      • It will give a plot using default values.
      • For example : What is the function of 01 04 ?
    • 4. What is the meaning of 01 04 ?
      • First number is the section number in upper box
      • Second number is the program number in lower box

    Go to Begin
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