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The bookUnit 1 · Sequences and Series of Functions9 / 83

Pointwise vs uniform convergence, M-test, Dini

Why this is asked: Uniform convergence is what lets you swap limit with integral/derivative/continuity. Compute sup|fₙ − f| explicitly; xⁿ, nx(1−x)ⁿ, nxe^{−nx²}, x/n are the recurring families.

Uniform convergence — what it buys and how to test it

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Check yourself — select all that apply

Let fn(x)=f_{n}(x) = nx(1x)n(1 - x)^{n} on [0, 1]. Which of the following are true?

Next: Power series, radius of convergence, Abel's theorem

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Open this in the full syllabus view · Unit 1