# 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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### Midpoint approximation over/under estimation

So left handed approximation underestimates the area under a increasing curve and over estimates for decreasing curves. And right handed approximation overestimates for increasing curves and ...
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Is there a way to approximate the convolution of Beta variables? Specifically, I am trying to find an approximation to $g(x_0)$: $$g(x_0) = \int \delta(x_0-\sum_{i=1}^{n} a_i x_i) \prod_{i=1}^{n} ... 1answer 193 views ### Find an upper bound on the absolute error of 3.141 as an approximation to π Q: Find an upper bound on the absolute error of 3.141 as an approximation to π I have no idea what to do... :( What I know: absolute error = real value - approximate value Help :) 3answers 421 views ### Approximating 1/z by polynomials Let C=\{\mathrm e^{\mathrm it}, 0\le t\le 3\pi/2\} and f(z)=1/z. By Runge's theorem, there is a sequence of polynomials p_n(z) such that$$\lim_n p_n(z)=f(z)$$uniformly on C. Does anyone ... 2answers 122 views ### How to approximate n \int_{0}^{1} [1 - x^m ]^n x^m dx  near infinity? I have a hypothesis that if:$$ I_{n,m} := n \int_{0}^{1} [1 - x^m ]^n x^m dx $$where m,n \in \mathbb{N} then$$ \lim_{n \rightarrow \infty} \frac{I_{n,m}}{n^{-\frac{1}{m} } } = c_m $$But I ... 1answer 99 views ### Approximating \tanh(B\sqrt{A} ) for small A and arbitrary B by correcting for asymptotic behaviour of \tanh I would like to approximate a function containing terms of the form \tanh( B\sqrt{A}) for small A. I have tried doing a Taylor series, but I consistently find that it is not only A that has to ... 1answer 70 views ### How do I show that these two definite integrals are approximately equal Consider the following two integrals: I_1=\int\limits_{0}^{1/x}G(s)\ ds I_2=\Big|\int\limits_0^\infty G(s)\exp[-ixs]\ ds\Big| where G(s) is a monotonically decreasing positive function, ... 1answer 30 views ### How to determine coefficients of p(x) = x^6 with the Chebyshev processing I want to calculate the coefficients of p(x) = x^6 with the Chebyshev processing. How to do that? Following question would be, how to estimate the error in [-1,1], if i only use terms until ... 1answer 45 views ### Asymptotic behaviour of the area of a 2-dimensional flat subset of \mathbb{R}^3 I am interested by the area of the 2-dimensional flat subset of \mathbb{R}^3 defined by the following equations with one parameter t>1: x,y,z>0 (positive octant) x+y+z=t (hyperplane ... 0answers 344 views ### Real approximation to the maximum using Laplace's method integral The Laplace's Method states that under some conditions, it holds that:  \sqrt{\frac{2\pi}{M(-g''(x_0))}} h(x_0) e^{M g(x_0)} \approx \int_a^b\! h(x) e^{M g(x)}\, dx \text { as } M\to\infty Where ... 4answers 142 views ### Approximation of \frac{1+a}{1+b} I've found the following assertion on an economics book: For r and g small enough, \frac{1+r}{1+g}\approx 1+r-g (where r is the interest rate and g is the growth rate of the economy) ... 1answer 50 views ### How to find a sequence by its limit? Is there any way to construct non-trivial sequence by its limit? Something like \begin{cases} a_1=2 & \\ a_{n+1}=\dfrac1{2}\left(a_n+\dfrac2{a_n}\right) \end{cases}for \sqrt2. I'm especially ... 2answers 116 views ### A curious partitions coincidence \sum_{n=0}^\infty P(n) q^{n+1}? Given the partition function P(n) and let q_k=e^{-k\pi/5}. What is the reason why,$$\sum_{n=0}^\infty P(n) q_2^{n+1}\approx\frac{1}{\sqrt{5}}\tag{1}\sum_{n=0}^\infty P(n) ...
By knowing that a discrete distribution of points go asymptotically to the density: $\displaystyle p(x)= \frac{1}{\pi \sqrt{1-x²}}$ in $[-1, 1]$ I am able to conclude that interpolating at those ...