Recognise that 𝑒 is the unique number 𝑎 for which the above limit is 1.

mm-u3-t1-s1-d2

Interactive

e — the one base whose limit is 1

manipulative

Slide the base a and watch (a^h − 1)/h settle on a level as h → 0; exactly one base makes that level 1, and that base is e.

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