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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Let nx 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