# zeno tsang

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bio website location China age member for 1 year, 6 months seen Jun 19 at 2:25 profile views 29

# 12 Questions

 7 $\forall x \in \mathbb{R}$, there exits $\delta$ such that $(x-\delta,x+\delta) \cap A$ is countable. Prove that $A$ is countable. 3 Compute $\int_0^\infty \frac{\ln x}{(1+x)^3}\,\mathrm{d}x$ 3 $0 < a_0 \leq a_1 \leq \cdots \leq a_n$, show $p_n(z) = a_0 z^n + a_1 z^{n-1} + \cdots + a_{n-1} z + a_n = 0$ has no root in $|z| < 1$ 3 $X$ and $Y$ are two topological spaces. $f$ is a surjection. For $A \subset X$, $(f(A))^0 \subset f(A^0)$. Show that $f$ is continuous. 2 $g(x) = x^3$, if $N$ is a null set on $\mathbb{R}$, can we conclude that $g^{-1}(N)$ is also a null set?

# 351 Reputation

 +15 Compute $\int_0^\infty \frac{\ln x}{(1+x)^3}\,\mathrm{d}x$ +15 Convergence of parametric series. +5 $X$ and $Y$ are two topological spaces. $f$ is a surjection. For $A \subset X$, $(f(A))^0 \subset f(A^0)$. Show that $f$ is continuous. +15 Prove that the following series do not converge absolutely

 3 Prove that the following series do not converge absolutely 1 Evaluate the integral using principal value and complex analysis 1 Differentiation of an infinite series of functions 0 Convergence of parametric series. 0 Prove that if f is a continuous strictly monotone function defined on an interval, then its inverse is also a continuous function.

# 15 Tags

 3 real-analysis × 9 1 derivatives 1 complex-analysis × 3 1 lebesgue-measure 1 measure-theory × 2 0 functional-analysis × 2 1 integration 0 general-topology × 2 1 improper-integrals 0 sequences-and-series × 2

# 2 Accounts

 Mathematics 351 rep 17 Stack Overflow 265 rep 18