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Prove that $(f_n)$, $f_n =x^n$, $x \in (0,1)$ is not uniformly convergent on $(0,1)$

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#real-analysis #proof-verification #uniform-convergence #sequence-of-function #pointwise-convergence
105
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Uniform convergence of digamma function

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#sequence-of-function #digamma-function
363
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Prove that $C_p[-\pi,\pi]$ is complete, knowing that $C[-\pi,\pi]$ is indeed complete

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#functional-analysis #continuity #complete-spaces #sequence-of-function
24
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Pointwise convergence of a sectionally defined function

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#real-analysis #sequences-and-series #proof-verification #sequence-of-function
58
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Uniform or pointwise convergence of a sequence of functions

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#real-analysis #proof-verification #uniform-convergence #sequence-of-function #pointwise-convergence
53
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Puntual and uniform convergence of function

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#sequences-and-series #convergence-divergence #uniform-convergence #sequence-of-function
41
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Uniform convergence of a sequence of functions 4

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#sequences-and-series #convergence-divergence #uniform-convergence #supremum-and-infimum #sequence-of-function
57
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Is it a continuous?

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#real-analysis #continuity #sequence-of-function
43
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Sum of an odd recursive sequence

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#sequences-and-series #summation #recursion #sequence-of-function
107
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Calculate $\lim_{n \to \infty} \int_0^1nx^nf(x)dx$.

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#real-analysis #calculus #analysis #uniform-convergence #sequence-of-function
132
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Proving that a sequence of functions has a convergent subsequence

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#functional-analysis #sequence-of-function
38
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Uniform Continuity implies boundedness in sequence of functions

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#real-analysis #uniform-convergence #sequence-of-function
413
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Uniform convergence in open intervals

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#real-analysis #sequences-and-series #uniform-convergence #sequence-of-function
107
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Calculate the limit of $\frac{n^{n+1}}{n!}\int_0^xe^{-nt}t^n\,\mathrm dt$

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#integration #limits #gamma-function #sequence-of-function
44
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Is there a sequence $(f_n)_n \subset C_b(\mathbb{R})$ with $f_n \to f \in C_b(\mathbb{R})$ pointwise but $f_n(1/n) \not \to f(0)$?

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#real-analysis #analysis #continuity #sequence-of-function

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