Mathematics Stack Exchange
Mathematics Stack Exchange

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.

4607 questions
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Find the approximate value of π

We re given a ruler, a compass and square sheets of side length $a$. Using these we need to find the approximate value of π. I tried to arrange the sheets similar to a graph paper. Then we can draw a circle of know (large) radius and approximately…
user579048
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Why do error models often contain "squares" of a value?

In many error minimization or approximation models, they often do operations on "sum of squares" of the calculated value. (E.G. residual sum of squares) What is the purpose of squaring the error? Is it to prevent negative values? If so, why not just…
Taylor
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Approximate a curve with limited number of samples

Preface: We have an analogue measurement device that changes its behaviour with temperature. We use an environmental chamber and cycle through a range of -20°C and 120°C to find out how the many components fluctuations with temperature affect the…
TheBeardedQuack
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Simple sig fig definition

The number $\tilde{p}$ is said to approximate $p$ to $t$ significant figures if $t$ is the largest non-negative integer for which $$\left|\frac{p-\tilde{p}}{p}\right| \le 5 \times 10^{-t}$$ Source Now, suppose the actual value $p$ is $1.0$ and…
hioqobipb
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If one rounds digits one by one starting from the end, then is the rounding same as when "cut-offing" around required the precision?

If one rounds digits one by one starting from the end, then is the rounding same as when "cut-offing" around required the precision? That is does (for $1/10^3$): $0.84562...4356 \rightarrow 0.8456 \rightarrow 0.846$ produce the same…
mavavilj
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Fractional Approx.

How to approximate $\frac{2*(10^3+10^6+1)}{(10^3 * 1001 *3)}$. In that problem Options are A) $\frac 35$ B) $\frac{33}{50}$ C) $\frac{333}{500}$ D) $\frac{3333}{5000}$ In that problem I got till above mentioned expression, but question was to…
Vivek
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Alternative to linear approximation for multiple points?

as a linear approximation is used to approximate a point between two points. how can we apply linear or other approximation when multiple points are given and we have to approximate a single point using all of them. For example as in linked picture…
Salman Shaukat
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Upper bound for $|\delta|$ in $1+\delta=\prod_{i=1}^n (1+\varepsilon_i)^{\pm1}$

I am trying to prove the following lemma: Let $|\varepsilon_i|\leq \varepsilon < \frac{1}{n} $ for all $1\leq i \leq n$ and define $\delta$ with $$1+\delta=\prod_{i=1}^n (1+\varepsilon_i)^{\pm1}$$ then $$|\delta| \leq…
B.Swan
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How is this approximation derived?

What is the argument behind: 1/(1+x) can be approximated by 1-x if x<<1 ? I couldn't find where this approximation comes from/derived.
floppy380
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Why is this equation only solvable by approximation?

In the following equation I am trying to solve for $\alpha$, where $F$ and $P$ are constants. $$P = e^{-\alpha/2}-\frac{1}{1+F}e^{-\alpha(1+F)/2}$$ Normally when I encounter an equation like this that I can't solve by simple algebra, I just stick it…
David K
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approximation on a graph

I expect my question to sound very naive, please excuse for this. I have a set of $(x, y)$ points on a graph, which are the measurements of a real-life process. Now I want to draw an "approximation line" (or "best-fit line", I don't know what is the…
yegor256
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Fractional Approximation of e^x

I am trying to obtain an approximation for $e^x$ of the form $\frac{ax+b}{cx+d}$ using the Maclaurin series for $e^x$. $\frac{ax+b}{cx+d}=e^x=1+x+\frac{x^2}{2}+\cdots\approx 1+x \\ ax+b = (1+x)(cx+d)=d+x(c+d)+cx^2\approx d+x(c+d) \\ 0 = (d-b) +…
Craig
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Using the Trapezoidal rule

QUESTION: I am doing this question using a tabular method of solving trapezoidal approx. and I came up with an answer as 1.1128153 but this answer is not on the above question answer list then I just assumed 1.56396455. please someone help me…
Surdz
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Numerical differentiation ( with second derivative)

$$ \begin{array}{c|c|c|c|c|c|c|c} t & 0 & 0.25 & 0.5 & 0.75 & 1 & 1.25 & 1.5\\ \hline x & 0 & 4.3 & 10.2 & 17.2 & 26.2 & 33.1& 39.1\\ \end{array} $$ $t$ is time in second and $x$ is distance in meter. I wanted to find the acceleration when $t =…
Thunfische
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Root mean square error of two functions

How can I calculate the root mean square error of two functions like \begin{align*} f(x) &= \sin(x)\\ g(x) &= x-\frac{1}{6}x^3 \end{align*} in $[0, 2\pi]$ range?
Shinzoo
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