# Tagged Questions

For questions that involve concrete approximations, such as finding an approximate value of a number with some precision. For questions that belong to the mathematical area of Approximation Theory, use (approximation-theory).

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### Montecarlo estimate of a integrand from 0 to $\infty$

I have a question about monte carlo estimation of integrals. Suppose I am told to estimate using monte carlo, the integral: $$f(y) = \int_{0}^{y}\frac{4}{1+x^{2}}dx$$ I want to estimate $f(\infty)$. I ...
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### Confusion about principles of decimal approximation

I ran into this paragraph in the introductory chapter on Taylor series of Morris Kline's "Calculus: An Intuitive And Physical Approach": "Thus, if the value of $\sin(x)$ for a particular value of $x$ ...
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### approximating functions via a piecewise combination of linear and constant functions

I am curious if anyone has encountered any literature on approximating functions via a piecewise combination of linear and constant functions. I have seen a couple of papers which use piecewise ...
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### Approximating statistics for huge dataset

I'm investigating users accounts statistics for Vkontakte social network. There are $N\approx2 \cdot 10^8$ accounts that have different metrics along them – boolean, discrete and continuous. I found ...
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### Approximation of a hypergeometirc-like distribution

Fix $0<\varepsilon<1$. For $m\in\mathbb{N}$, let $$c_m=\max\left\{\frac{{m-1\choose s-1}{m\choose k-s}}{{2m\choose k}}:\;k=1,2,\dots,2m(1-\varepsilon)\;\mbox{and}\;s=1,2,\dots,k\right\}$$ Prove ...
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### Explain why $\exp(-7 \log_{10} n)$ approximates $1/n^3$ so well

I was graphing a few functions, and discovered that the graphs of $\exp(-7 \log_{10} n)$ approximates $1/n^3$ are almost the same. Can anyone explain why this is so? Is there a general result for this ...
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### Intergral approximation?

For the integral: $$I=\int^{t/2}_{-t/2} e^{i(\omega_1-\omega_2)t'}dt'$$ What would be the lower limit on $t$ for the approximation: $$I\approx 2\pi \delta(\omega_1-\omega_2)$$ to hold? I would guess (...
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### Find alternative shortest paths given extra properties

This is a follow-up question for a question I asked at here. The problem is mapped to a graph with say non-negative weights on edges (no preference if it can be directed or not). However, along with a ...
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### Interpolating sequence problem.

Below is a question which I cannot quite figure out. Any tips would help appreciated!I've been working on this for about a month. "Let $(z_j)$ be a sequence of distinct points in a domain $D$ that ...
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### Taylor expansion of this electric field

I'm trying to determine what happens when R>>z for the below equation $\frac{z\sigma}{2\varepsilon }\left ( \frac{1}{z}-\frac{1}{\sqrt{R^{2}+z^{2}}} \right )$ Like most books, which is a great ...
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