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).

Approximations are representations of numbers that aren't exact, for example $\sqrt{2}\approx 1.41$. Such representations may be obtained using differentials (more generally, Taylor's formula), linear interpolation, etc.

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The "best" simple and accurate approximation for $x - \cos(x) = w$

the given equation is $x-\cos(x) = w$ given some $w$ values $-100, -1.9827359827356, 50, 75.2982735, 100\ldots$ maybe many more between, say $-10000\ldots 10000$ Please find some a) simple !! b) enough accurate approximation to find $x$ I…
Ytrewq
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Approximating $\ln(2)$ with error of $5*10^{-3}$?

How many terms of $ln(2)=1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}$ are needed to approximate it with an error of less than $5*10^{-3}$?
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