Reading a Limit Off a Table, and Knowing What It Proves

You'll learnto build a table that closes in on a target from both sides, to read the estimate off where the columns agree rather than off the last row, and to know what a finite table can and cannot prove.

A table is the most direct way to watch a limit happen: pick inputs marching toward the target, read the outputs, and see what they settle on. It is also the easiest place to fool yourself, because a table that stopped too early looks just like one that has settled. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · SAMPLE BOTH SIDES AND GO CLOSE · v2

two columns close in from opposite sides · read where they agree

Before you start

What you're looking at

One graph and one table showing the same thing twice: two dots walk in toward a target and the table fills in a row for every place they stop.

The question

What value are the two columns settling on, and how would you know they have settled?

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