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## USING A TABLE OF VALUES TO ESTIMATE A LIMIT

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**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 ModeSettings**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.**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**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**NewValue 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,**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,**We see that the limit from the right and the limit from the**left seem to be equal. So we conclude that