Honestly, e belongs in a calculus course, not in algebra 2. Presenting it prematurely makes it seem magical and incomprehensible. Why the rush to get e in before students are ready for it?
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The complete works of Lagrange are readily available online, and they're an absolute delight to read (if you read French.) The exposition I refer to here is in his calculus textbook, perhaps the first ever designed for use by college students, which occupies Vol 9 of the Oeuvres.
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Lagrange's approach artfully downplays the limiting operation (indeed, it was his contention that this operation is not needed for the proper formulation of the calculus!) and does many marvelous things with "high school algebra" alone. Breathtaking brilliancies everywhere.
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