# Landscape

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Selected questions with my answers(to be updated):

Interesting unanswered questions(to be updated):

# 188 Posts

 21h answered $(x+2)\cos\frac1{x+2} - x\cos\frac1x > 2$ for $x\in[1,\infty)$ 2d answered What is my operator norm (cannot get good enough bounds). May19 answered If $f(x)\to 0$ as $x\to\infty$ and $f''$ is bounded, show that $f'(x)\to0$ as $x\to\infty$ May19 answered Comparing the value of $\int _0 ^{\frac{\pi}{2}} x^n \sin^nx\,dx$ for different $n$ May18 answered Harmonic Function bounded by a linear function May16 answered Application of Open Mapping Theorem May16 answered Zeros of a cubic polynomial with rational coefficients May16 answered $P(|X|\ge\lambda a)\ge (1-\lambda)^2a^2$ for $0\le \lambda \le 1$ May16 answered Error bounds for $e$ May14 answered singularity of analytic continuation of $f(z) = \sum_{n=1}^\infty \frac{z^n}{n^2}$ May13 answered Prove that $c^3f(c)+c f(c)\ge1$ May13 answered Property of partial traces May12 answered How to prove that there exists a $z_0 \in U_{1} [0]$ such $\prod_{k=1}^{n} |z_0 - a_k | \geq 1$ for $a_1, \dots , a_n \in U_{1} [0]$? May12 answered slowness of growth of polynomials May11 answered Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$? May11 answered Riemann surface arising as a quotient of the upper half-plane. May10 answered proof using pigeonhole principle May10 answered Choosing a linear map $(\mathbb{Z}/2\mathbb{Z})^n \rightarrow \mathbb{Z}/2\mathbb{Z}$ which is nonzero on half of a sequence of vectors May9 answered Sum of eigenvalues and singular values May9 answered The sum of the series $\sum_{n=0}^{\infty}\frac{\epsilon_n}{n!}$ is an irrational number