### Questions (66)

 7 $f$ is monotonically increasing, $0 \le f \le 1$ and $\int_0^1 (f(x) - x) dx = 0$ then $\int_0^1|f(x)-x|dx \le \frac{1}{2}$. 6 If $f^2(t) \le 1+2\int_0^tf(s)\mathrm{d}s$ prove $f(t)\le 1+t$ 6 How to prove the existence and uniqueness of the solution of a second order linear ODE? 5 Hartshorne's Exercise II.4.5(c). A third time. 4 $\int f^2$ and $\int f''^2$ is convergent then so is $\int f'^2$

### Reputation (1,334)

 +20 Define homology by simplicial Eilenberg Maclane spectra. +10 Hartshorne's Exercise II.4.5(c). A third time. +10 The multiplicity of a root $r$ of a irreducible polynomial is a power of $p$ characteristic +10 When is $x^a\sin (x^{-b})$ $\alpha$-Hölder Continuous on $[0,1]$?

 16 Calculating the exponential of an upper triangular matrix 5 How to prove $\int_0^1\sin(x+\frac{1}{x}) \, dx$ is convergent? 2 Clarification of L'Hopital Proof Pugh 2 Is it true that $A_x$ has even order for all $x\in G$? 1 Variety of Connected Components

### Tags (82)

 16 matrices 2 abstract-algebra × 9 16 matrix-exponential 2 finite-groups × 3 5 calculus 2 group-theory × 3 3 algebraic-geometry × 23 1 algebraic-groups × 3 3 real-analysis × 5 1 deformation-theory × 2

### Bookmarks (4)

 7 Convergence of $(\sin x)^x$ 3 How do I find $\left|\langle a,b\mid a^2=b^3=e\rangle\right|$? 3 How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple? 2 Positive forms and strongly positive forms are bidual