# Questions tagged [approximation]

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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### Different approximations of this function

Was told to post here. However, I have heard about this site, as well, but I am hesitant on posting on the internet, hence I made an account. Anyway, my question is: How can I approximate the sin(2) ≈...
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### Is there a way to represent functions using circles, similar to how Taylor series work?

I was curious whether or not there is a method of representing a function as an infinite amount of circles multiplied or added or something? Similar to a Taylor series, such that the method would ...
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### Why $\pi$ appears in Dirac? [duplicate]

"With hands", what is the reason why $\pi$ appears in this result : $\lim_{\epsilon\to 0}\frac{\epsilon}{\epsilon^2+x^2}=\pi\delta(x)$
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### How the following Approximation is done to obtain the Inverse Laplace Transform?

The following highlighted part from a textbook is where I am stuck. The Laplace transform is independent of the derivations made prior to equation $(2.77)$. Please help me to understand how they have ...
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### Second order Taylor approximation

$$\log E_t(X_{t+1}) = E_t(\log X_{t+1}) + \frac{1}{2}Var_t(\log X_{t+1})$$ How can I prove it?I knwe that, $$g(x) = g(E(x))\ +\ g'(E[x])\ (x-E[x]) + \ g''(E[x])(x-E[x])^2$$ But I do not know how to ...
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### Where does this relation come from? $n^2-1 \approx (n-1)2$ for $n-1 \ll 1$

I came across the relation in the title in a physics textbook and wondered how I get to it. $$n^2-1 \approx (n-1)2$$ for $$n-1\ll 1$$ Could anybody maybe help me out? Thanks!
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### Can you identify this unknown sequence related to approximating circle area using unit squares?

I am interested in finding out whether the following sequence has already been "discovered" or if it is worth submitting to OEIS (Online Encyclopedia of Integer Sequences), since I can't find it on ...
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### Finding the interval of a function that can be approximated to $x^3$

$f(x) = \ln(1+x^2) \cdot \arctan(x)$ Using the approximation $f(x) = x^3$ Find the interval centered at zero where this approximation is accurate to within $0.00001$, or $10^{-5}$ So I know that ...
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### Set Cover Problem: How to calculate the denominator?

I am trying to understand the set cover problem. I found the algorithm at: Set Cover which also contains the attached example: Somebody please guide me, how we calculate the denominator |S-C| and how ...