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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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Normal approximation of binomial distribution.

The probability that a shooter strikes a target is 0.4. By using a suitable approximation,find the probability that he will strike the target 220 times out of 500 shots.
Mun Yee
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Find the approximation with Gamma function

Let $n$ postive integer,Assmue that $\Gamma(x)$ is Gamma function $$\dfrac{\Gamma\left(\dfrac{1}{2}+\dfrac{1}{2n}\right)}{\Gamma\left(1+\dfrac{1}{2n}\right)}=A+\dfrac{B}{n}+\dfrac{C}{n^2}+\dfrac{D}{n^3}+\cdots$$ use…
math110
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How to find the first-order approximation around a given point?

Lets pretend i have some function $f(x) = 2*x_1 + 3*x_2$, and says find first order approximation around some point [a b]. I know the formula $f_a (x) = f(x') + f(x)'*(x-x')$, but do not know how to plug in 2 dimensional point in place of x' By the…
ASROMA
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Population growth approximation

Suppose I am studying the evolution of a system of unicellular organims and I want to have a continuous model of its population $\,\mathrm{P}\left(t\right)$ with respect to a real time variable $t$ ( units: days ). We make the assumption that there…
Dory
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$.0030077$ radians is $\arctan(.0030077)$ degrees?

$.0030077$ radians is $\arctan(.0030077)$ degrees? In this question Related Rates Hot Air Balloon, the op converts from radians to degrees, by taking the $\arctan(\text{radians})$. This is obviously a wrong method. In fact if your calculator is set…
Ahmed S. Attaalla
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Approximately equal too symbol operations permitted

I have to doubt to clear if A is approximately to 2/3 B can I write it as A approximately equal to 4/6 B? Since it is approximate relation is it permitted to multiply both numerator and denominator as with equal to relationship?
joe1983
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Approximate (but as accurate as it can) location of sound

I quess that this is relatively easy question, but I have been struggling this for a two days now (basicly investigating different formulas) and couldn't find a solution. So, let's think this case: Three (or more) internet nerds from same area (like…
cyberseppo
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Find the linearization of the function at 0

The problem asks: Find the linearization of $f(x)= \sqrt{a+bx} $ at $0$ To get all parts of $L(x) \approx f(c) - f'(c)(x-c)$ I've done: $$f(0) = \sqrt{a}$$ $$f'(0) = {b\over 2\sqrt{a}} $$ Now: $$L \approx \sqrt{a} + {b\over 2\sqrt{a}}(x-0)$$ $$=…
FakeBrain
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Prove that if $2a^2 - b^2 = \pm1$ then $\frac ba \approx \sqrt2$

Prove that if $2a^2 - b^2 = \pm1$ then $\frac ba\approx\sqrt2 $ (a,b) (1,1),(2,3),(5,7),(12,17),(29,41),(70,99)....
Yu. K
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desintegration constant

I have this system in maple and I can't get it work write: sist:=diff(x(t), t) =-k*x(t), x(0)=x0; Can someone help me get the desintegration constant k if the half-time is t1/2=700*10^6 Thanks
John Smith
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Find value of a variable from measured data

I have a measurement from which I want to deduct the value of a physical size (velocity). The theoretical equation is $$ A\frac{(b+vt)^2}{(c-vt)^2} $$ Where $A$, $b$ and $c$ are all known sizes, $t$ is the time variable and $v$ is the wanted size.…
SIMEL
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How to approximate the division by a number like prime number?

I was solving some mathematical questions and have come across the situation, where I need to divide 3900/139. Here is my question, a. Can I assume 139 to 140 for the ease of division? If so, how will I know what percentage of error I am…
dexterous
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$x$ln$x$ quadratic approximation at $x=1$

$x$ln$x$ quadratic approximation at $x=1$ 2 ways : 1) quadratic approx whole thing : $(x-1)^2 + \dfrac {(x-1)^2} 2$ This isn't same as 2) split $x$ and take quad approx of ln$x$ at $x=1$ $x((x-1) - \dfrac 1 2 (x-1)^2) = x(2x - \dfrac 3 2)$ Why…
zcahfg2
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Approximating fractions

I have a fraction $\dfrac{a}{b}$ where $a$ and $b$ are both two large integers with $30$ digits each. I wish to approximate this fraction with a new fraction $\dfrac{c}{d}$ where $c$ and $d$ are both $10$-digit integers. I came up with two…
Héctor van den Boorn
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Eliminating order notation in upper bound

I have that some value $E_i=\alpha^2\varepsilon_i^3+O(\varepsilon_i^4)$, where $\alpha>0$ is a fixed constant and for every $i$, $0<\varepsilon_i\ll1$. I would like to place an upper bound on $E_i$ that does not include the term $O(\varepsilon_i^4)$…
Albert Fletcher
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