Extremal

### Questions (232)

 18 How to recognize a finitely generated abelian group as a product of cyclic groups. 11 $C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$. 11 Prove that there exist linear functionals $L_1, L_2$ on $X$ 9 Prove that $|f|\leq 1$ whenever $|x|\leq 1$. 8 Find an element of largest order in the symmetric group $S_{10}$.

### Reputation (3,204)

 +10 Dimension of garden to minimize cost +10 Find the matrix $S$ such that $A=S^{-1}JS$. +5 Computing $\int_0^{2\pi} \frac{1}{a^2\cos^2 t+b^2 \sin^2 t} dt \;; a,b>0$. +5 Show that $\hat{\mu}(t)$ is of the form $e^{\lambda t^2}$

 6 Prove if sup $S \in S \Rightarrow$ sup $S =$ max $S$ 5 How to integrate $\frac{x^n}{1+x}$ 4 $x^2 +x -2 \geq 0$ basic problem 4 Find the limit of $\lim\limits_{x\rightarrow0}\frac{x}{\tan x}$. 3 The equation $a^2 - 4b = 3$ has no integer solution

### Tags (161)

 24 calculus × 34 9 proof-verification × 4 11 limits × 5 8 linear-algebra × 19 10 real-analysis × 59 8 algebra-precalculus × 4 10 derivatives × 14 6 elementary-number-theory × 3 9 integration × 13 5 matrices × 13

### Accounts (2)

 Mathematics 3,204 rep 1728 English Language & Usage 101 rep 1