First, enter the formula for f(x) in your graphing calculator (or the on-line function utility) as

(Notice the parentheses. Why are they there? If you're not too sure, press choice buttons B, C, and D above to see the effect of omitting one or both sets of parentheses. (Also consult Applied Calculus, Section A.1 for some further examples of formula entry.)

Using this formula, we can use the TABLE feature on the TI-82 or TI-83 to complete the given table as

x approaching 3 from the left     x approaching 3 from the right
x
2.9
2.99
2.999
2.9999
f(x) =
x2+x-12

x - 3
6.9
6.99
6.999
6.9999
3
3.0001
3.001
3.01
3.1
7.0001
7.001
7.01
7.1

Noticing that, as x approaches 3 from either side, f(x) approaches 7.0, we can conclude that the limit is (approximately) 7.0.

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