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Posts tagged 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 5mo ago by Grove‭ · edited 7d 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 9d 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 11d ago by Pavel Kocourek‭

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

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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 $

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

Question real-analysis improper-integral

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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 2mo ago by Snoopy‭ · last activity 2mo 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 12mo ago by whybecause‭ · last activity 12mo 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 12mo ago by whybecause‭ · last activity 12mo 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 1y ago by whybecause‭ · last activity 1y 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 1y ago by whybecause‭ · edited 1y 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 1y ago by deleted user · last activity 1y 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 1y ago by deleted user · edited 1y 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 1y ago by deleted user · edited 1y ago by deleted user

Question calculus real-analysis differentiation