Mathematics
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amsmath
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question
28
$ I(r) = \int_0^{2\pi}\frac{\cos(t) - r}{1 - 2r\cos t + r^2}\,dt$ is always zero for $r\in[0,1)$. Why?
Jan 26, 2019
answer
12
Calculating the integral with an undefined function f(x)
Mar 5, 2021
question
11
If $f : [a,b]\to\Bbb R$ is continuous, are there $x_1,x_2\in (a,b)$ such that $\tfrac{f(b)-f(a)}{b-a} = \tfrac{f(x_1)-f(x_2)}{x_1-x_2}$?
Sep 14, 2018
answer
9
How to find the limit of series? (What should I know?)
Oct 29, 2017
answer
9
How do I prove that $|\det(A+B)|\leq2^n$ where $A,B$ are $n\times n$ unitary matrices?
Oct 16, 2019
answer
8
Show that $A^{-1} + B^{-1}$ is invertible when $A,B$ and $A+B$ are invertible
Mar 27, 2019
question
7
Continuity with respect to Hausdorff metric, also with intersection?
Feb 25, 2021
answer
7
$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.
Mar 28, 2019
question
7
Given $A\in\Bbb R^{n\times n}$, is $C_A := \{SAS^{-1} : S\in GL(n,\mathbb R)\}$ connected?
Jul 20, 2018
answer
7
Calculate $\lim_{x\to 0} {1\over x} \int_0^x \cos(t^2)\,dt$
Oct 28, 2019
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