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RISC World

Locus

Another exclusive Foundation RISCWorld application

Exercise 3. More on Zooms and Rescaling.

Ensure that Locus is set up as follows.

  1. 'auto-scaling' should be 'on'.
  2. 'squaring up' should be 'off'
  3. Set the domain to -0.1<x<0.1

Now draw the graph of y=xsin(1/x) (this can be found on the formula menu.)

This is a fascinating function which becomes interesting for values of x which are very close to zero, so we shall use the manual zoom facility to see what it looks like close to zero.

  1. Click on the icon showing a picture of a magnifying glass and a plus sign.
  2. Click <Select> and hold at the point (-0.002,0.003)
  3. Drag the box to the right and down to the point (0.002,-0.003)
  4. Release the mouse button.
  5. Zoom in a few more times to see what happens.

Because of the way Locus works you may find that the oscillations become wild and inaccurate. It would take a very long time to plot every point on the graph and this would normally not be necessary. However there are times when accuracy is desirable.

In the middle of the top row of buttons you will see a writable icon flanked by a pair of 'bump' icons. This should normally contain a number in the range 128-512. This is the Plot Step value. (For more information see the manual). If you are drawing graphs with lots of asymptotes or wild oscillations then this number should be large, but the larger the value the more slowly the graph will be drawn.

Clicking on the small, triangular, button arrow to the right of this icon increases the number and clicking on the similar button on the left decreases the number.

Click on the right hand button until the number rises to 4096 (you can do this by typing the number if you prefer.) and then click on the <Plot> icon. You should see an immediate change in plotting speed but also note the change in accuracy.

If you want to zoom out again you can use the negative zoom button but it is best to reduce the plotting step first so that this does not take too long.

If you get bored waiting for the graph to plot, then pressing ESCAPE will stop the plot and return control to the user.

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