Mathematics - Posts tagged real-analysis

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Q&A Does the series $\sum_{n=1}^{\infty} \frac{n^n}{n!} e^{-n}$ converge?

2 answers · posted 7mo ago by Snoopy‭ · last activity 7mo ago by Snoopy‭

Question calculus real-analysis series

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Q&A Find the value of $\sum_{k=1}^\infty\frac{k^2}{k!}$

3 answers · posted 8mo ago by Snoopy‭ · last activity 8mo ago by Derek Elkins‭

Question complex-analysis real-analysis series

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Q&A What does it mean by saying that $C([0,1])$ is a subset of $L^\infty([0,1])$?

2 answers · posted 1y ago by Snoopy‭ · last activity 8mo ago by celtschk‭

Question real-analysis

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Q&A Example of $f:[0,1]\to\mathbf{R}$ with $\lim_{a\to 0^+}\int_a^1f(x)dx=L $ for some real number $L$ but $\int_0^1|f(x)|dx=\infty $

2 answers · posted 2y ago by Snoopy‭ · last activity 8mo ago by Michael Hardy‭

Question real-analysis improper-integral

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Q&A The derivatives of a function at a boundary point

2 answers · posted 1y ago by tommi‭ · last activity 8mo ago by Michael Hardy‭

Question derivatives real-analysis

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Q&A $\liminf (a_n+b_n) = \liminf(a_n)+\liminf(b_n)$ provided that $\lim a_n$ exists

1 answer · posted 1y ago by Snoopy‭ · last activity 8mo ago by Snoopy‭

Question real-analysis limits

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Q&A Cyclical or “loop” fractals?

2 answers · posted 1y ago by Julius H.‭ · last activity 11mo ago by pbloem‭

Question real-analysis fractal

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Q&A Using convexity in the proof of Hölder’s inequality

1 answer · posted 1y ago by Snoopy‭ · last activity 12mo ago by Snoopy‭

Question real-analysis

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Q&A Fourier transform of an $L^1$ function is uniformly continuous

1 answer · posted 1y ago by Snoopy‭ · edited 1y ago by Snoopy‭

Question real-analysis fourier-analysis

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Q&A For any real number $m$, $ \left|\sum_{n=1}^{\infty}\frac{m}{n^2+m^2}\right|<\frac{\pi}{2} $

1 answer · posted 1y ago by Snoopy‭ · last activity 1y ago by Snoopy‭

Question calculus real-analysis

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Q&A If both $\lim_{x\to\infty}f(x)$ and $\lim_{x\to\infty}f'(x)$ exist, then $\lim_{x\to\infty}f'(x)=0$.

1 answer · posted 1y ago by Snoopy‭ · last activity 1y ago by Snoopy‭

Question real-analysis

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Q&A $\sup(A\cdot B) = (\sup A)(\sup B)$ where $A$ and $B$ bounded sets of positive real numbers

3 answers · posted 1y ago by Snoopy‭ · edited 1y ago by Snoopy‭

Question real-analysis supremum-infimum

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Q&A Why is $ \int_0^{\infty}\left|\frac{\sin x}{x}\right|\ dx=\infty$?

1 answer · posted 1y ago by Snoopy‭ · last activity 1y ago by Snoopy‭

Question real-analysis improper-integral

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Q&A Classification for involutory real infinite series

1 answer · posted 1y ago by nsajko‭ · last activity 1y ago by Peter Taylor‭

Question classification real-analysis inverse polynomials series

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Q&A Which other Real Analysis textbooks unusually recommend ending delta-epsilon proofs with a cluttered, bedecked $\epsilon$? [closed]

0 answers · posted 2y ago by TextKit‭ · closed 2y ago by Mithical‭

Question real-analysis

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Q&A Is $f(x)=\sin(x)$ the unique function satisfying $f'(0)=1$ and $f^{(n)}(\Bbb R)\subset [-1,1]$ for all $n=0,1,\ldots$?

1 answer · posted 2y ago by Grove‭ · edited 2y ago by Pavel Kocourek‭

Question derivatives real-analysis

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Q&A Is there a "regular" quasi-convex function $f:\Bbb R^2 \to \Bbb R$ that is not a monotone transformation of any convex function?

0 answers · posted 2y ago by Pavel Kocourek‭

Question multivariable-calculus real-analysis convex-analysis monotone-functions

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Q&A Is there a two variable quartic polynomial with two strict local minima and no other critical point?

0 answers · posted 2y ago by Pavel Kocourek‭

Question multivariable-calculus real-analysis maxima-minima polynomials roots

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Q&A Finding the limit $ \lim_{x\to 0^+}e^{1/x}\sum_{n=\lfloor 1/x\rfloor}^\infty\frac{x^n}{n} $

1 answer · posted 2y ago by Snoopy‭ · last activity 2y ago by r~~‭

Question real-analysis limits

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Q&A Is it impossible to prove Jensen's inequality by way of step functions?

1 answer · posted 3y ago by whybecause‭ · last activity 3y ago by whybecause‭

Question real-analysis convex-analysis Jensen's-inequality

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Q&A "Pointwise equicontinuity implies uniform" implies compact

1 answer · posted 3y ago by whybecause‭ · last activity 3y ago by whybecause‭

Question real-analysis equicontinuity continuity metric-spaces

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Q&A $\{f_n\}\to f$ in $X$ implies $||f||\le\liminf||f_n||$

1 answer · posted 3y ago by whybecause‭ · last activity 3y ago by whybecause‭

Question real-analysis functionals normed-vector-space

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Q&A $\int_{E_n} |g|^q = \left| \int_E \chi_{E_n}\cdot \text{sgn}(g)\cdot g \cdot |g|^{q-1}\cdot |g| \right|$

0 answers · posted 3y ago by whybecause‭ · edited 3y ago by Derek Elkins‭

Question real-analysis Lp-space

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Q&A Find the intervals on which it is increasing and those on which it is decreasing of the following function.

1 answer · posted 3y ago by deleted user · last activity 3y ago by deleted user

Question calculus derivatives real-analysis functions maxima-minima

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Q&A Rules of checking differentiability for Rolle's theorem

0 answers · posted 3y ago by deleted user · edited 3y ago by deleted user

Question calculus real-analysis limits differentiability rolle's-theorem

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Q&A Second mean value theorem proof (differentiation)

0 answers · posted 3y ago by deleted user · edited 3y ago by deleted user

Question calculus real-analysis differentiation

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Posts tagged real-analysis