# Une Femme Douce

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# 654 Questions

 32 To show that the set point distant by 1 of a compact set has Lebesgue measure $0$ 20 Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$ 16 There exist an infinite subset $S\subseteq\mathbb{R}^3$ such that any three vectors in $S$ are linearly independent. 14 How to show path-connectedness of $GL(n,\mathbb{C})$ 13 I need to calculate $x^{50}$ [duplicate]

# 12,388 Reputation

 +10 Some closed subspace of $l_2$? +5 $u,v,w\in V\ni \|u\|=\|v\|=\|w\|=2,\langle u,v\rangle=0,\langle u,w\rangle=1,\langle v,w\rangle=-1$ +5 $A\in M_4(\mathbb{C}) \ni A^3=A^2\ne 0$ and rank$(A)=2$, $A$ is not diagonalizable also. +10 Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$

 30 Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$ 12 $AB-BA=I$ having no solutions 9 If $2^x=3^y=6^{-z}$ then prove that:$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$ 7 Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$? 6 Let $f$ be an analytic function such that if $|z|=\frac{1}{2}$ then $f(z)\in \mathbb{R}$. Prove that $f$ is constant.

# 153 Tags

 90 real-analysis × 195 34 integration × 10 74 calculus × 39 30 linear-algebra × 130 57 general-topology × 122 30 indefinite-integrals × 2 56 complex-analysis × 154 26 limits × 21 34 group-theory × 48 26 functions × 16

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