State which of the following is true. 1. If a sequence of functions (fn)n converges pointwisely to f on [a, b], then fndr → Li sdr . 2. If a sequence of functions (fn)n converges pointwisely to f on [a, b], then (fm)n converges pointwisely to f' . 3. If a sequence of functions (fm)n converges uniformly to f on [a, b), then fndr → Si fdr . 4. If a sequence of functions (fn)n satisfies Indx → L fdr, then (fn)n converges uni- formly to f on [a, b).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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State which of the following is true.
1. If a sequence of functions (fn)n converges pointwisely to f on [a, b], then fndr →
Li Sdz .
2. If a sequence of functions (fn)n converges pointwisely to f on [a, b], then (fm)n converges
pointwisely to f' .
3. If a sequence of functions (fn)n converges uniformly to f on [a, b), then fndr →
Si fdx .
4. If a sequence of functions (fn)n satisfies fndx fdx, then (fn)n converges uni-
formly to f on [a,b).
Transcribed Image Text:State which of the following is true. 1. If a sequence of functions (fn)n converges pointwisely to f on [a, b], then fndr → Li Sdz . 2. If a sequence of functions (fn)n converges pointwisely to f on [a, b], then (fm)n converges pointwisely to f' . 3. If a sequence of functions (fn)n converges uniformly to f on [a, b), then fndr → Si fdx . 4. If a sequence of functions (fn)n satisfies fndx fdx, then (fn)n converges uni- formly to f on [a,b).
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