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Pointwise/Uniform Convergence of Sequence of Functions (and continuity!)

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#sequences-and-series #uniform-convergence
150
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Proving uniform convergence of a Series

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#real-analysis #sequences-and-series #uniform-convergence
167
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Uniform Convergence and limit $(n+1)\int_0^1 x^nf(x) \; dx$

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#real-analysis #uniform-convergence
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if $ L = \lim_{x\to1^-} \sum_{n=1}^\infty a_nx^n$ then $\sum_{n=1}^\infty a_n = L$

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#convergence-divergence #uniform-convergence
129
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$ \sum_{n=0}^\infty a_ne^{-\alpha_nx} $ converges for $x_0$ prove it uniformly converges in $[x_0,\infty]$

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#real-analysis #sequences-and-series #convergence-divergence #uniform-convergence
136
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Sequence of functions that converge uniformly on a compact metric space.

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#convergence-divergence #uniform-convergence
114
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Finding a particular type of sequence of functions

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#real-analysis #sequences-and-series #analysis #soft-question #uniform-convergence
225
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Given $f_n:= e^{-n(nx-1)^2} $, any suggested approaches for showing that $\lim_{n \to \infty}\int^1_0 f_n(x)dx = 0$?

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#real-analysis #integration #definite-integrals #uniform-convergence
123
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How to show that $\sum\limits^\infty_{n=0}a_n(\frac{2x}{1+x})^n$ is continuous?

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#real-analysis #sequences-and-series #uniform-convergence
120
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Limits of Sequences of functions and uniform convergence 3

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#real-analysis #uniform-convergence
105
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Geometry of Analysis

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#real-analysis #geometry #uniform-convergence #uniform-continuity
28
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A question uniform convergence

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#real-analysis #general-topology #uniform-convergence
215
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Proving if $\frac{nx}{e^{nx}}$ converges uniformly

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#uniform-convergence
63
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Calculating values of integrals using Fourier series and uniform convergence

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#definite-integrals #fourier-series #uniform-convergence
191
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How to prove that this series converges uniformly?

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#sequences-and-series #fourier-series #uniform-convergence

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