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As in the first part of this lab, we will use an ellipse with
axes 6/5 and 1 as our basic example.
QUESTION 6:
If you have not already done so, define
M := sqrt(1-(5*x/6)^2);
then issue the special Maple command:
gridplot2d(x=-2..2,y=-1..1, grid=[10,10],region=-M..M);
(Hint: you may want to ``constrain'' the resulting image so that
the horizontal and vertical scales are the same.)
- Use the displayed
grid to compute a lower bound on the area
of the indicated ellipse. Explain what method you used to approximate the
area.
- Compute an upper bound for the area. Again, explain your method.
- Sketch a picture (use 2 colors!) indicating the geometry behind your
two answers.
QUESTION 7:
The special Maple command leftbox2d computes the area by adding up the
area of all boxes in a grid whose lower left corner is contained in a region.
- Compute an approximation to the area of the previous ellipse by using
the command
leftbox2d( 1, x=-2..2,y=-1..1, grid=[10,10], region=-M..M);
- Try to determine if
this method of approximation produce an upper bound or a lower
bound for the area of the ellipse. Again, illustrate
your answer with a picture.
Bob Hesse
Thu Feb 20 09:21:36 CST 1997