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Mathematics
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xldd
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11
Why does $\int_{-x}^x f^\alpha\leq f(-x)+f(x)$ imply $f=0$?
Jun 26, 2022
9
Proving the existence of $ξ$ and $η$ such that $f'(\xi)(\xi-a)+f'(\eta)(\eta-b)+f(a)+f(b)=0$
Jun 10, 2021
8
Prove that $\int_0^\frac{\pi}{4}\frac{\cos (n-2)x}{\cos^nx}dx=\frac{1}{n-1}2^\frac{n-1}{2}\sin\frac{(n-1)\pi}{4}$
Mar 27, 2022
8
$D: \Bbb R[x]\to \Bbb R[x]$ satisfies $D(fg)=D(f)g+fD(g), D(x)=1$.Can we show that $D$ is linear?
Jan 3, 2023
7
$\int_0^1 tf(2x-t)dt=\frac{1}{2}\arctan(x^2), f(1)=1$, find $\int_0^1 f(x)dx$. here $f$ is continuous.
Dec 4, 2021
7
$\lim_{n\to\infty}\int_0^\infty \frac{f(x)}{x^2}\sin nx dx=\frac{\pi}{2}f'(0)$
Sep 23, 2022
7
Proving that $\sum_{n=1}^{\infty}\left (\left|a_{n}\right|+\left|b_{n}\right|\right) <\infty $.
Apr 1
6
$A,B$ are real matrices, similiar in complex field, then they are similar in the real field.
Dec 16, 2022
5
Profile decomposition of $f$ satisfying $\lim_{x\to\infty}[f(x+a)-f(x)]=0$, for any $a\geq 0$.
Aug 5, 2021
4
$f(x+1)=f(x)+1$ for monotone continuous $f$ defined on $\Bbb R$, $g_n(x)=f^n(x)-x$, show $\lim_{n\to\infty}\frac{g_n(x)}{n}$ is independent of $x$.
Jan 7, 2022