Theoretical Computer Science
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Jozef
  • Member for 11 years, 5 months
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8
Motivation for Developing Shortest Path Simplex Algorithms
Nov 17, 2012
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43
Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
36
Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
30
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
29
An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$.
29
Prove: $\int_0^1 \frac{\ln x }{x-1} d x=\sum_1^\infty \frac{1}{n^2}$

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