Maisam Hedyelloo
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 19 Evaluating the derivative of $\large \;e^{e^x}$? 13 Do $AB$ and $BA$ have same minimal and characteristic polynomials? 11 Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$ 9 Proving that $\int_a^b\frac{dx}{\sqrt{(x-a)(b-x)}}=\pi$ 8 If two functions go to infinity at zero, does the difference go to zero?

### Reputation (6,581)

 +5 A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian? +5 Finite multiplicative group of matrices with sum of traces equal to zero. +5 Maximal ideals in the ring of real functions on $[0,1]$ +5 Questions about $1-$ form $\beta$ on $(M,\alpha)$ such that satisfies $\nabla\beta(X,Y)=|| \beta^\sharp||^2 \alpha(X,Y)-\beta(X)\beta(Y)$

### Questions (101)

 23 How to prove that $\frac{(5m)!(5n)!}{(m!)(n!)(3m+n)!(3n+m)!}$ is a natural number? 18 How to compute the series $\sum\limits_{x=0}^\infty\sum\limits_{y=0}^\infty\sum\limits_{z=0}^\infty\frac{1}{2^x(2^{x+y}+2^{x+z}+2^{z+y})}$ 18 How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer? 18 If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$. 17 How to prove summation, multiplication, subtraction of two roots of $1+x+\frac{x^2}{2!}+\cdots+\frac{x^p}{p!}=0$ aren't rationals?

### Tags (101)

 91 calculus × 35 22 inequality × 13 57 linear-algebra × 51 20 differential-equations × 18 42 matrices × 29 15 algebra-precalculus × 10 29 integration × 24 15 trigonometry × 8 25 derivatives × 2 14 real-analysis × 10

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