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On a sequence of continuous functions

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#real-analysis #derivatives #solution-verification #sequence-of-function #baire-category
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Show that $\{x \in X: \sup_{i} f_i(x) > r \}= \bigcup_{i} \{x \in X : f_i(x) >r \}.$

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#real-analysis #supremum-and-infimum #sequence-of-function
32
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Is a sample statistic a random sequence?

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#probability #sequences-and-series #statistics #random-variables #sequence-of-function
54
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Does adding two functions with carry always converge?

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#functions #convergence-divergence #sequence-of-function
230
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Calculate the next value?

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#sequence-of-function
112
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Combining limits in analysis

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#real-analysis #sequences-and-series #limits #limits-without-lhopital #sequence-of-function
134
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Point wise convergence and differentiation counter examples

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#real-analysis #analysis #derivatives #uniform-convergence #sequence-of-function
181
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$\liminf (f_n+g_n)=\liminf f_n + \liminf g_n$

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#supremum-and-infimum #limsup-and-liminf #sequence-of-function
18
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Does uniform convergence of a series implies pointwise *absolutely* convergence?

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#sequences-and-series #sequence-of-function
39
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Controlling power series by a function

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#calculus #sequences-and-series #power-series #sequence-of-function
49
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Constant for a given limit

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#real-analysis #sequences-and-series #limits #analysis #sequence-of-function
817
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Uniform Convergence of $\sin(x/n)$ in $\Bbb{R}$

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#uniform-convergence #sequence-of-function
166
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How to prove uniform convergence

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#functions #uniform-convergence #sequence-of-function
71
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To find the limit of a sequence

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#real-analysis #sequences-and-series #analysis #cauchy-sequences #sequence-of-function
57
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For $n=1,2,3,\cdots $, $f_n(x)=\frac{2nx^{n-1}}{1+x}$ for $x\in [0,1]$ then $\lim_{n\to \infty}\int_0^1f_n(x)=?$

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#real-analysis #sequence-of-function

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