The applet shall provide quick access to the forms
 of graphs, but cannot replace understanding.

 Some applications to different mathematical topics:

 1. Enter linear and quadratic functions! Determine
     the coordinates of intersection points by using
     the zoom option, and by doing the computation!

 2. Enter the expressions
     x^2
     2 - x^2
     and
     x !
     Are there points in which all three graphs meet?
     Analyze the situation using the zoom option,
     and carry out the computation!

 3. The graph of the function
     f(x) =
     x^2 - 2
     is a
     parabola. Its zeros are sqrt(2) and - sqrt(2).
     By zooming towards the positive zero, you may
     determine sqrt(2) with high accuracy. After
     some magnification steps, the first few digits
     of the x-value remain constant. This shows how
     close you are already to the zero.
sqrt(2)=
 1.4142135623730950488016887242096980785696718753769480731766797379907325

 4. How many solutions has the equation
     x^3 - 2*x + 1
     = 0,
     and what are their numerical values?

 5. Consider the function
     f(x) =
     x^2
     and zoom-in
     towards some region on its graph! After some
     magnifications, you will be unable to
     distinguish the graph from a straight line.
     Functions whose graphs display no kinks may
     `locally´ be approximated by linear functions
     (whose graphs are straight lines). This fact
     is important when it comes to differential
     calculus.

 6. The function
     f(x) =
     sin(10*x) + sin(9*x)
     is the
     superposition of two oscillations with similar
     (though non-equal) frequencies. How does the
     graph look like? Which acoustic effect does it
     correspond to?

 7. Clarify the form of the graph of the function
     f(x) =
     sin(x) + sin(100*x)/100
     by looking at it closely! Can you explain its
     behaviour?
     [Same with f(x) =
      sin(x) + sin(100*x)/10
     ].

 8. Study the function
     f(x) =
     (sin(9*x)+sin(10*x))*sin(0.1*x)
     by means of the zoom option! Can you explain the
     behaviour of the graph?

 9. The function
     f(x) =
     exp(-x^2)
     plays an important
     role in statistics. Can you explain the form of
     its graph?
     [Same question for f(x) =
       2^(-x^2)
     in case you
     don't know the exp function].

 10. Can you explain the form of the graph of the
      function
      f(x) =
      x*3^(-x^2)
      ?

 11. A very interesting topic is the behaviour of
      the function
      f(x) =
      x*sin(1/x)
      near x=0.
      Due to the finite pixel size, the graph becomes
      biased after some magnification steps, but
      the essential features may still be observed.

Above is home site example file. Freeman isolate
the useable equation to a single line. User can
copy a line. The expression [ x ! ] does not work.

=====

Program use online source. If Home site change their
files, this program will stop work. 2006-07-15-22-56.

To keep a working copy, save next three files
in same folder. File name "fplotter.jar" and
file name "a_fplotter.class" must not change.

2006-07-13-22-28-54 maths online funktion plotter
http://www.univie.ac.at/future.media/moe/fplotter/fplotter.html
save as
C:\$fm\js\javaplot\fplotter.html

2006-07-14-09-02-09
http://www.univie.ac.at/future.media/moe/fplotter/fplotter.jar
save as
C:\$fm\js\javaplot\fplotter.jar

2006-07-14-09-02-59
http://www.univie.ac.at/future.media/moe/fplotter/a_fplotter.class
save as
C:\$fm\js\javaplot\a_fplotter.class

After save files to local computer hard drive,
open fplotter.html it should work.
If home site change file, you still have a working copy.
If home site update file, you still have a outdated copy!
2006-07-15-23-20


2006-07-16-11-08
The file you download from
http://www.univie.ac.at/future.media/moe/fplotter/fplotter.html
This file use
[[
<APPLET
 archive="fplotter.jar"
 code="a_fplotter.class"
.....
]]
and no
<base href=http://www.univie.ac.at/future.media/moe/fplotter/>
which is just right. You can work off line.
(Because  fplotter.html
 and      fplotter.jar
 and      a_fplotter.class
 are in one folder.
)

On the other hand, if you save
http://freeman2.com/graph04e.htm
to your hard drive. graph04e.htm is designed to work
online. If you want to use graph04e.htm for off line. 
In "graph04e.htm" please delete next line
<base href=http://www.univie.ac.at/future.media/moe/fplotter/>
then "graph04e.htm" will look for (in same folder)
fplotter.jar
a_fplotter.class
instead of
http://www.univie.ac.at/future.media/moe/fplotter/fplotter.jar
http://www.univie.ac.at/future.media/moe/fplotter/a_fplotter.class

fplotter.jar
and
a_fplotter.class
are files you already saved to your hard drive.
and are in same folder as graph04e.htm
2006-07-16-11-21




This page URL
http://freeman2.com/graph04e.htm

First upload 2006-07-16

Thank you for visiting this page.

Freeman 2006-07-16-00-00