Fractions Definition and 606 Threads

Homework Statement The problem is from Stewart, Appendix G, A58, no.45. Suppose that F, G, and Q are polynomials, and: F(x)/Q(x) = G(x)/Q(x) for all x except when Q(x) = 0. Prove that F(x) = G(x) for all x. [Hint: Use Continuity] The Attempt at a Solution I thought the statement was...

I have a question regarding various planes in an FCC, and determine their packing fractions. I searched but couldn't find anything :) For example, one of the planes is the (100) plane, and I have said there are 2 full atoms (1 in the middle, and 4 quarters from each side), distance 'a'...

Hi! There's this one problem that I'm having troubles with. I've tried using the decomposition method, but I've ended up getting a messy answer. If someone can give me tips or the solution to the problem, I'll appreciate it. Here's the problem: solve the integral of 1/ y^2-1 dx.

Homework Statement http://books.google.com/books?id=qFNZIUQ_MYUC&pg=PA142&lpg=PA142&dq=loren+larsen+%224.3+23%22&source=web&ots=YKlIl_yPb3&sig=MC2QCtuBii9za-vd4FkAJadZ_dI I am working on 4.3.23b) I can get that \sum_{i=1}^n \frac{g(x_i)}{f'(x_i)}\frac{1}{x-x_i} = g(x)/f(x) but I do not...

is there any quick way to convert numbers to fractions then back to decimals, without changing the mode. also if i type in log 54, it gives me log 54. i don't get an answer even if i put in ln 32 it gives me ln 32, not an answer. i've learned to input functional equations and make...

I'm dealing with the fraction: 1+1 1+1/(1+1) 1+1/(1+1/(1+1)) ... After viewing another similar forum I found that they came up with the equation (k+or-sqar(k^2+4))/2 Which here is (1+or-sqar(5))/2 My question is how did they derive that equation? I need to show proof of that...

For example..without a calculator is there any easy way to find the value of \frac{1}{19} or any fraction in which the denominator ends in a '9' ?

Check out the link to see the problem and my work. Can anyone see where I made an error? I can't seem to figure out where I went wrong. https://www.physicsforums.com/attachment.php?attachmentid=11519&stc=1&d=1194912644"

I have a question about congruences involving fractions. For integers a and b the following is defined: a and b are congruent modulo m (m is a natural number) if there exists an integer k such that k*m = a-b a \equiv b (\mbox{mod } m) \Longleftrightarrow \exists k \in \mathbb{Z} : km = a-b...

Evaluate the integral of x^2-x/(x^2-1)^2 from 0 to 1. * I know that I have to use partial fractions in order to make the integral integratable. My attempt at partial fractions: A/(x-1) + (B/(x+1)) + (Cx+D/(x^2-1)^2) Is this setup right? (Once I have it set up correctly, I know how...

Homework Statement I am given 9/[(s-1)(s-1)(s-4)] as part of a Laplace Transform. I'm supposed to decompose into partial fractions. Homework Equations So 9/[(s-1)(s-1)(s-4)]= D/(s-1)+E/(s-1)+F/(s-4) The Attempt at a Solution To simplify: 9= D(s-1)(s-4)+ E(s-1)(s-4)+ F(s-1)^2...

Please help with the following question: http://img161.imageshack.us/img161/691/continuousfraction5az5.gif By considering other values of k, determine a generalized statement for the exact value of any such continued fraction. For which values of k does the generalised statement hold...

Arc Length, Irreducible quadratic factors i'm having a hard time seeing this method, and i have to use this method on one of the problems I'm doing to find it's Arc Length. L=\int_{\sqrt{2}}^{\sqrt{1+e^{2}}}\frac{v^{2}dv}{v^{2}-1}} the book suggests to first divide then use a...

I have a homework question that reads: Represent the following rational functions as sums of elementary fractions and find the primitive functions ( indefinite integrals ); (a) f(z)=z-2/z^2+1 But my confusion arrises when I read sums of elementary fractions. I think what the question is...

Homework Statement I don't understand something I have read about partial fractions so I wonder if anyone can help! To each repeated linear factor in the denominator of the form (x-a)^2, there correspond partial fractions of the form : A/(x-a) + B/(x-a)^2 Is this true if we have...

I don't fully understand the logic of this example: For, 4x^2-3x+5/(x-1)^2(x+2) we need: A/(x-1)^2+B/(x-1)+C/(x+2) It is also correct to write Ax+B/(x-1)^2 + C/(x+2) but the fractions are not then reduced to the simplest form. How do the 2nd fractions simplify to give the 1st set of...

I have two... Homework Statement The the limit Homework Equations \lim_{x \rightarrow 1} \frac{1-cosx}{x^2} The Attempt at a Solution I figured to just plug in 1, but I wanted to make sure... Homework Statement Find the limit Homework Equations \lim_{x \rightarrow 3}...

Heres a question I am stuck with Crosslinked polymers consisting of 62 wt% ethylene and 38 wt% propylene may have elastic properties similar those for natural rubber. For a copolymer of this composition, determine the fraction of the ethylene mer. Express your answer with three decimal...

It says in my book that a any function can be decomposed to some sum of strictly proper rational functions where the denominator of each rational function is either consist of linear functions, irreducible quadratic functions. "Any proper rational function can be expressed as a sum of...

Need a check on the last problem of my test: integral (3x^2-8x+13)/(x^3+x^2-5x+3) Factor for the denom is (x-1)(x-1)(x+3). So a/(x-1) + b/(x-1)^2 + c/(x+3) = the f(x) in the integral Factor out and multiply all the polynomials. Comes down to a = -1, b = -2, c = 2 Integral...

Homework Statement Hello, I just found a question, and having attempted it many times I get different answers, probably due to my messy working, however I have just tried it twice again and got the same answer, just checking with you guys to see if you think it is correct. Thanks...

Im going to Durham uni in oct to do physics, and the nice people of the physics department sent me some maths questions to do before I arrive. One of the partial fractions questions looked simple enough, but when I did it, I got it wrong...so with the answer they give, i worked back to the...

f(x) is a polynomial. A product of n distinct factors (x-a_{i}). Prove that \frac{1}{f(x)}=\sum\frac{1}{f'(a_{i})}.\frac{1}{(x-a_{i})} This I can do by writing f(x)=(x-a)g(x) where g(a)<>0. Then splitting \frac{1}{f(x)} into \frac{A}{(x-a)}+\frac{h(x)}{g(x)} for some...

I'm having a bit of trouble with fraction multiplication. I understand the concept visually, but don't understand why the mechanical multiplication method works the way it does. Please bear with my descriptions, I'm just learning fractions (as well as basic math operations)and want to show how...

The following is a well-known unsolved problem : If n is an integer larger than 1, must there be integers x, y, and z, such that 4/n=1/x+1/y+1/z? A number of the form 1/x where x is an integer is called an Egyptian fraction. Thus, we want to know if 4/n is always the sum of three...

Homework Statement [(3x^2)+10x+13]/[(x-1)([x^2]+4x+8)] Homework Equations I think solving this question should include partial fractions. The Attempt at a Solution I've made a few different attempts at this question but find myself at a dead end every time. One attempt was...

Evaluate each factorial expression A) (n+2)!/n! My book doesn't really show how to come up with a solution. After looking in the back for the answer it showed (n+2)(n+1), which works if you plug in random values for x. "After" seeing the answer I reasoned maybe it could be broken down as...

Homework Statement I just want to know how to proceed to get 1/s - s/(s^2+1) using partial fractions on the term 1/(s(s^2 − 1)) I know this is probably straight forward but I just don't get it. Thanks.

Homework Statement Find an expression for the nth Term: { 1/3, 1, 7/5, 5/3, 13/7 } Homework Equations The Attempt at a Solution The problem has obviously had its fractions reduced on almost every case if not every case. I've been working on this problem for at least 4...

Hi, my question is given the recurrence relation for the convergents, could we construct a continued fraction so.. \alpha = a_{0}+ \frac{b_{0}}{a_{1}+\frac{b_{1}}{a_{2}}+... all the coefficients a's and b's are equal to a certain integer ? for example if all the coefficients...

The problem is \int \frac{2s+2}{(s^2+1)(s-1)^3} dx What I'm wondering about is there anyway to get the partial fractions out without doing the full mess of bringing up the (s^2+1) and (s-1)^3 ? I tried the heaviside method and got one of the numerators but I'm stuck for a practical way to do...

From http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub049.html : "Using one of the algorithms, which is based on an identity involving Bessel functions, gamma has been computed to 30,100 decimal places. By computing their regular continued fractions, we show that, if gamma or...

for any function f(x) how can you convert it to continued fractions in the form: \frac{a_{0}+a_{1}x+a_{2}x^{2}+...}{b_{0}+b_{1}x+b_{2}x^{2}+...} where we must determine the a(n) and b(n) if f(x)=x^{1/2} i know how to do it.

Just got a new TI-89 Titanium, can't really figure it out yet, I need help changing decimals to fractions, and fractions to decimals fast. Any ideas?

Homework Statement the question can be ignored - it involves laplace and Z transforms of RLC ckts. Vc(s) = 0.2 ----------------- s^2 + 0.2s + 1 find the partial fraction equivalent such that it is : -j(0.1005) + j (0.1005) --------------...

if you have \frac{3s + 1}{(s+2)^2 + 4^2} does it become... 3s + 1 = \frac{A}{(s+2)} + \frac{B}{(s+2)^2} + \frac{C}{4} + \frac{D}{4^2} or... 3s + 1 = \frac{A}{(s+2)} + \frac{B}{(s+2)^2} + \frac{C}{4^2}

Homework Statement integrate((x^3+72)/(x^2+6x+8))dx Homework Equations The Attempt at a Solution I decided to use partial fractions method. x^2+6x+8 factors to (x+4)(x+2) x^3+72=A(x+2)+B(x+4) when A=-2, 64=B(2), B=32 when B=-4, 8=A(-2), A=-4 -4*int(1/(x+4)) +...

Homework Statement I need to integrate this differential equation using partial fractions to obtain an equation for P in terms of t; P(t): 1/P dP/dt = b + aP Homework Equations The Attempt at a Solution So far, this is what I have: ln /P/ = bP + aP^2/2 +c...

I have: \frac{(1+j\omega)(3-j\omega)}{(3+j\omega)(3-j\omega)} When I perform the partial fraction expansion I get: \frac{-2}{3+j\omega} Where my calculator gets: 1 - \frac{-2}{3+j\omega} . Why am I wrong? I am performing the expansion as follows: \bar F(s) =...

Homework Statement http://server6.theimagehosting.com/image.php?img=fractions.JPG Can someone please give me the methodology/rules for this to happen? Homework Equations N/A The Attempt at a Solution I know there is nothing you can factor out here so I am confused as to how this...

Homework Statement Suppose that a town has a population of 100,000 people. One day it is discovered that 1200 people have a highly contagious disease. At that time the disease is spreading at a rate of 472 new infections per day. Let N(t) be the number of people (in thousands) infected on...

Homework Statement Give the formula in terms of tn+1 for the continued fraction: http://www.math.sunysb.edu/posterproject/www/images/continued-fraction.gif and so on... Homework Equations The Attempt at a Solution I got the recursive formula:tn+1=1+(1/tn), but I need the explicit formula

how do you do that

Hi Guys, can anyone help with this problem? resolve 3 -x ---------------- (x^2 +3) (x + 3) The problem I have is with the x^2, when substituting numbers for x at the end to find A and B. I can only use -3

I'm trying to understand how fractions relate in total resistance. You have parrell circuits. Each one has a 2 ohm resistor on it. FOr if you go by the law 1/total resistance = N/sum of resistances. SO that gives us 1/total=2/1 It we make the 2 a 1 that means the 1 becomes 1/2. SO that...

dumb partial fractions question... suppose i get x+1=A(x-2)+B(x-2) how do you then find A and B?

I have never remebered the different partial fraction forumlas. Is there a way to decide which partial fraction formula to use just by looking at the expression?

Is there an algorithm which can convert any rational number to a sum of distinct unit fractions which minimizes the number of terms or the largest denominator?

Given that \frac{dx}{dt} = k(a-x)(b-x) : (a) Assuming a \neq b , find x as a function of t . Use the fact that the initial concentration of C is 0. (b) Find x(t) assuming that a = b . How does this expression for x(t) simplify if it is known that [C] = \frac{a}{2} after 20...

Problem with factorising Hi, the question is to differentiate the following equation with respect to x. x^4(3x-1)^3 Using the product rule i think i'v partially completed this to x^4(3(3x-1)^2) + (3x-1)^3(4x^3) I'm now required to simplify this - which leaves me completely stumped...