Approximate Definition and 174 Threads

I get the many proofs behind it and all of the mechanics of how to use it. What I don't get is why it works.. What was the though process of Brook Taylor when he devised his thing? I get that each new term is literally being added to previous ones along the y-axis to approximate the y value of...

Homework Statement I need to approximate the number 14.45 to nearest integer. Homework Equations The Attempt at a Solution If I remember correctly, to approximate a decimal up to say 2nd decimal place, I look at the third digit and if this is greater than or equal to 5, then I...

Homework Statement If X^2=Sqrt(x1^2+x2^2+x3^2+...)=> X? and vice versa If X=x1+x2+x3+...=> X^2? Homework Equations The Attempt at a Solution

Homework Statement Here is the problem with the solution:http://dl.dropbox.com/u/64325990/MATH%20253/Capture.PNG I don't understand how dV is the error. Isn't the error the actual value - the estimated value? In other words, ΔV-dV?

【what] does it mean by the term" approximate to four decimal place accuracy" hey I have a question. What does it mean by the term " approximate to four decimal place accuracy". For instance, I want to approximate cos(pi/5) to four decimal place using the macluarin series. The actual value of...

Suppose I had the equation xx = i How would you go about approximating the thing? Is there a way to graph this on the complex plane?

Homework Statement Homework Equations The Attempt at a Solution

Please give only hints, no full solutions :) Homework Statement Use series to approximate the definite integral to within the indicated accuracy: \int_0^{0.1} \frac{dx}{\sqrt{1 + x^3}}, |\text{error}| < 10^{-8} Homework Equations Taylor series and Maclaurin series The Attempt at a Solution...

Never Mind I answered my own question two minutes after posting it. I don't know how to take this question down so I just deleted it.

Dear all, I am struggling to understand a simple integration problem. Here is my integration: Integration [0, t] {d S(u) / r(u)} My friend says that above integration can be approximately written as Sum [ti <= t] {si / ri} S is the step function increasing by si at each step...

Since it has a decimal it would be 20kg * 9.8m/s which equals 196kg m/s^2 = 196N But the decimal means i have to round two sig figs, which would make it 200N? A very simple problem, I really don't know why I'm asking it.

[SIZE="3"]Homework Statement Determine an expression for the Bohr radius (a_{0} from the following approximation. The electron moves to the nucleus to lower its potential energy, V(r) = -\frac{e^{2}}{r} If the electron is in domain 0\leqr\leq\bar{r}, then we may write...

I want to have the following function approximated (in elementary functions) within a error of 1e-6: (x^2+a^2)^{1/4}\ \forall x\ \in [-1,1],\ a\in \mathbb{R} If I use Legendre polynomials I have to use a lot to get convergence (since if I use an estimate of the error the error decreases with...

Homework Statement This is a problem from an old exam I am reviewing for practice. Find a good approximation, for x large and positive to the solution of the following equation: y''-(3/x)y'+(15/(4x^2)+x^(1/2))y=0 Hint: remove first derivative term Homework Equations The...

Homework Statement What is the approximate uncertainty in the area of a circle of radius 5.3 * 104 cm? Express your answer using one significant figure. Homework Equations A = pi*r2 The Attempt at a Solution Using the given radius, I found the area to be 8.8 * 109 cm2. And since...

I am trying to reproduce the results of a colleague and I am having difficulty understanding how to find a PDF of a data set. The calculations were preformed on a chemical system and the energy for a 1000 random orientation of the molecule was calculated. Am I right in thinking that if I plot...

Hi, I'm an indie game developer working on a free online puzzle/simulation game set in space. The object of the game is to move, resize, push, pull and otherwise manipulate celestial bodies to solve problems, like putting a planet in a stable orbit or accelerating a satellite to near...

I'm working on this differential equation this few days... Could you give some guidance on approximate solutions to it? i(t) is the only function while all others are parameters. \frac{di(t)}{dt} = -\lambda(\sigma\phi\sqrt{i(t)(1-i(t))} + N\mu i(t)(1-i(t)) Thank you a lot!

Hello every one, now I'm dealing with a series a(k) = k^(-s)e^(-tk), s,t > 0 I want to find a continuous function to approximate the partial sum, S(n)of it. I hope there can be a good approximation. Please help me find it, thanks!

Concerning Hardy-Littlewood approximate functional equation for the \zeta function \zeta(s) = \sum_{n\leq x}\frac{1}{n^s} \ + \ \chi(s) \ \sum_{n\leq y}\frac{1}{n^{1-s}} \ + \ O(x^{-\sigma}+ \ |t|^{\frac{1}{2}-\sigma}y^{\sigma - 1}) does somebody know of any similar result for the...

[PLAIN]http://img600.imageshack.us/img600/1210/11096142.png Hey I was wondering if you guys could help me out with this question... I think I have the right power series: = \frac{1}{1-x} + \frac{x}{1-x} = (1+x+x^{2}+x^{3}+...)(x+x^{2}+x^{3}+x^{4}+...) = 1+2x+2x^{2}+2x^{3}+2x^{4}+... = 1 +...

The following is an approximation problem. Given a ratio: D =\frac{ \sum a_ib_i}{\sum b_ib_i} I wonder what steps to follow to give a reasonable approximation. This is an intuition D =\frac{ \sum a_i}{\sum b_i}. Clearly, given that all b_i terms are the same, the approximation is the...

The Questions Let y(x) be the position of a particle at time x. Suppose that we know that the velocity of a particle satisfies the differential equation: y'(t) = ty with y(0) = 1. We will try to give a reasonable method to approximate some of the positions of the particle. a.)...

Hey there, i´m dealing with a problem when I´m trying to analyze an arch bridge for approximate stresses in the arch. The normal force is quite easy to get for such structure. The problem I´m running into is the fix-end moment for the arch under both dead load and live load (live load is...

what is meant by the custodial SU(2) approximate symmetry as a 5, a 3? it is always mentioned in the Higgs triplet, charged higgs context.

I'm trying to calculate the error of the Trapezoid Method in my population approximations for wolves and moose over time given certain parameters. Ultimately what i need to do is perform a series of trapezoid approximations using different 'h' values. Each successive 'h' value I use is half...

Hello, I need help with this problem. I need to find the first three terms of the Taylor series for the function f(x)= (1 + x)^(1/3) to get an estimate for 1.06^(1/3). Hence I did: f(x)= (1 + x)^(1/3) f'(x)= (1/3)(1 + x)^(-2/3) f''(x)= (-2/9)(1 + x)^(-5/3) f(a) + f'(x)/1! * (x - a) +...

Homework Statement 1. The Table below lists the isotopes of Pb and their percent by mass: Isotope % Mass 82p, 122n 1.37% 82p, 124n 26.25% 82p, 125n 20.82% 82p, 126n 51.55%(a) Using these data, calculate the approximate atomic mass...

Suppose f(n,p)=integral(n!/(x! (n - x)!dx, for x from -1/2 to p) where n>1, p<n+1/2 Are approximate formulas known for this kind of integral? Empirically, f(n,n+1/2) seems to be close to 2^n More generally, I'm looking for approximate formulas for integrals of n!/(x1!x2!...xn!) over nice...

Many authors and lecturers use the word approximate. It is not mathematically to say something is close to another... I'm wondering what is the definition of approximate.

You can obtain a rough estimate of the size of a molecule with the following simple experiment: Let a droplet of oil spread out on a fairly large but smooth water surface. The resulting ”oil slick” that forms on the surface of the water will be approximately one molecule thick. Given an oil...

I'm a bit confused, i have a question, it asks me to find ''the absolute relative approximate error'' at the end of each iteration. What's the formula of ''the absolute relative approximate error''?

Homework Statement Kirchoff's first law gives the relationship E(t) = L * (di/dt) + R*i where L is the inductance, R is the resistance and i is the current. \begin{tabular}{|c|c|c|c|c|c|} \hline $\emph{t}$ & 1.00 & 1.01 & 1.02 & 1.03 & 1.04\\ \hline $\emph{i}$ & 3.10 & 3.12 & 3.14 &...

how do you find the approximate uncertainty of a circle of radius 3.8x10^4? Homework Statement how do you find the approx uncertainty for a circle with radius 3.8x10^4, i have no idea how to get the final uncertainty of the circle the radius uncertainty is 0.1x10^4 area of a circle is...

I have a ton of homework with square roots of complex numbers. Like sqrt(2 + 3i) What is the fastest way to break these down into its approximates like 1.67 + 0.895i without using a TI89/Maple/Matlab/Mathmatica.

Homework Statement Consider the harmonic scillator potential perturbed by a small cubic term, so that V(x) = \frac{1}{2}m\omega^{2} (x^{2} - \frac{x^{3}}{a}) if a is large compared to the characteristic dimension (\hbar /m\omega)^{1/2}, the states will all me metastable, since there can be no...

I'm interested in knowing if there are any techniques besides taylor series and picards method to find approximate general solutions to non-linear ordinary differential equations. I'm not interested in numerical techniques only algebraic approximations.

Homework Statement question: approximate the function f if the ratio R_1 / R_2 is about 1000. given: the van der pauw equation for resistivity: \rho = ( pi * d / ln[2] ) * (R_1 + R_2})/2 * f(R_1 / R_2), where f is a function of the ratio R_1/R_2 only and satisfies the relation...

I have 2 questions: 1. When there are no fermion mass terms, the Dirac part of the Lagrangian posseses an SU(N) left X SU(N) right flavour symmetry for N flavours of fermions. This can be "re-arranged" as an SU(N) vector X SU(N) axial symmetry. The axial part is spontaneously broken by the...

Homework Statement This is technically an E&M question, but I've reduced it to a calculus problem. Basically I have to evaluate: B_0(\int_{-H_{max}}^{H_{max}}{tanh(\frac{H+H_c}{H_0})dH - \int_{-H_{max}}^{H_{max}}{tanh(\frac{H-H_c}{H_0})dH) Where H_{max}>>H_C, H_0.Homework Equations The...

Hi, Why is it that the WKB approximation produces the correct eigenvalues for the Harmonic Oscillator problem, but the wrong wavefunctions, whereas for the square well, we get correct wavefunctions and the wrong eigenvalues? I've been trying to dig through the approximations we make in...

Homework Statement Estimate the approximate maximum deflection of the electron beam near the center of a CRT television screen due to the Earth's field. Assume the screen is 20 from the electron gun, where the electrons are accelerated by the following voltages. Note that in color TV sets...

How do I go about finishing/calculating this? Homework Statement Use a power series to approximate \int\cos 4x\log x dx to six decimal places. (bounds are from pi to 2pi) Homework Equations The Attempt at a Solution So I broke down the equation first: \int\cos 4x\log x dx =...

I've found this site that states: "The surface gravity on Mars is only about 38% of the surface gravity on Earth." So a 100 lbs object will weigh about 38 lbs or a 45.359 kg will be on Mars 17.237 kg (converting 38 lbs in kg). So to find the Fg of Mars, I did this kind of equation...

I'm interested in coming up with an function that approximates the solution to a non-linear differential equation. (There is no known closed form solution) The equation is Y''=(1/Y)(Y')^2-Y*A+Y^2*A where "A" is a constant, and Y' and Y'' are the first and second derivatives with respect to...

Homework Statement This isn't really even a homework question..i've just been reviewing some general math concepts and this one has been driving me nuts..i haven't done math in a while. At time t = 1, a particle is located at position (1,3). If it moves in a velocity field F(x,y) =...

Hello Ive come across some approximate cross section formulas during a course of particle physics. And in a reaction like A + B --> R --> C + D the cross section should be something like \sigma = K\frac{\Gamma_R^{AB}\Gamma_R^{CD}}{(s-m_R^2)^2+m_R^2\Gamma_R^2} Where K is a constant (depending...

I got a relation as follow \lambda_k = \frac{2 n(\lambda_k) L}{k} where \lambda_k is a wavelength at mode k, k is integer, n is the index of reflection, L is a constant. I am trying to find the change of wavelength between two adjacent mode approximately, the answer will be...

Hello all. This problem is mostly math based, but is being applied to a programming algorithm. I'm working on a problem with a massive amount of normalized vectors in a massive amount of dimensions and need to quickly compute the nearest neighbors of anyone vector. More precisely, I need to...

Calculate the approximate frequency of the C-H bond, with the force constant of k = 500 N/m. Use: Frequency = (1/2pi) Sqrt(k/((m1m2)/(m1 m2))) BUTT WHAT DO I USE FOR MY MASS VALUES?? I tried, 12.011g/mol and 1.01g/mol and that is incorrect.