USING A TABLE OF VALUES TO

ESTIMATE A LIMIT

Use a table of values to estimate

x 0

x 4 2lim .

x

Set Derive to

Approximate Mode

with 15 digits .(See next 4 slides.)

On the menu at the top of the Derive screen

•click Options•then click Mode Settings

In the Mode field under Precision, click the arrow; click Approximate.

Find the Digits field and change the number in this field to, say, 15.

Then click the OK button.

Now type the formula into the editing line. Then click Enter.

Now create a list of positive values of x that are approaching 0.

I will use the following values:

.1, .01, .001, .0001, .00001, .000001

Substitute these values, in turn, for x in the formula

x 4 2

x

Make sure the formula is highlighted on the Derive screen.

On the top toolbar (second line from the top) click the Sub(Substitute)

button.

In the box that now appears, find the New Value field and type .1.

Then click Simplify.

Derive now displays the answer.

Now click the formula on the Derive screen to highlight it again.

Then repeat the previous substitute procedure for each of the remaining

values of x in the list.

You should see the following decimals.

Notice that these results seem to be approaching the number 0.25, that is,

1

4 .

Repeat the substitute procedure for a list of negative values of x that

are approaching 0.

I will use the following values:

-.1, -.01, -.001, -.0001, -.00001, -.000001

You should obtain the following results:

Notice that these results also seem to be

approaching the number 0.25, that is, 1

4.

So we conclude that

x 0

x 4 2 1lim 0.25 .

x 4

We see that the limit from the right and the limit from the left seem to be equal.