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Taylor/Maclaurin Series

Infinite twins of familiar functions · BC Calculus · greeting

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Owl · Mock interview — Taylor/Maclaurin Series. I ask; you answer.

Owl · Caveat: the series equals the function only where it converges to that function — not automatically on all of ℝ for every f. We'll write core series, recognize them, and manipulate carefully.

Larry’s gold answer — Show text to read it out loud.

Larry · gold answer · Maclaurin for eˣ should be Σ xⁿ/n! from n = 0 to ∞. For sin x I expect x − x³/3! + x⁵/5! − …

Owl: Caveat: the series equals the function only where it converges to that function — not automatically on all of ℝ for every f. We'll write core series, recognize them, and manipulate carefully.

You: —