Fraction Definition and 640 Threads

Homework Statement I basically need to find the integral of (-5x^3-1x^2+4)/(x^4+2x^3) Homework Equations Just the basic rules associated with partial fractions when re-writing a polynomial with constants. The Attempt at a Solution Since the degree of the denominator is 4 and...

Hi there! 1)It's a very common problem for me . I don't get when do I have to multiply or divide a fraction in unitary method e.g. 10 men do 1 work in 40 days 10 men does 3/4 work in 40*3/4 days or should i do 10 men does 3/4 work in 40*4/3 days I do't undestand!Plz give me a reason...

Homework Statement If i have 1/2 + 1 = 1,5 (on the calculator), how do i make this into a fraction? I know this answer would be 1/2 + 1 = 3/2 But how excactly is this done? Homework Equations The Attempt at a Solution

Homework Statement Solve for t: [-2(t2+1) / 9(t2-1)] < 0 The Attempt at a Solution I know that the answer is -inf<t<-1 and 1<t<inf, but how do I show the calculation to get that answer? When I tried, I narrowed it down to t<root-1, but that's not possible (without complex...

Ok, so why do some answers contain an A/something + (Bx + C)/something and others contain just an A/something + B/something. I hope someone knows what I'm talking about!

Homework Statement integral using partial fraction Hi everyone ,, got the following question : The attempt at a solution I reached the following ,, integral ( 4/(X^2+x+1) + (-4x-1)/(X^2+x+1)^2) ) and now I don't know how to integrate .. -_- help please

Homework Statement Very pure liquid water can be subcooled at atmospheric pressure to temperatures well below 0ºC. Assume that 1kg has been cooled as a liquid to -6ºC. A small ice crystal (negligible mass) is added to "seed" the subcooled liquid. If the subsequent change occurs adiabatically...

contrary to AGW theory. I have not yet read the actual study. http://bristol.ac.uk/news/2009/6649.html"

Homework Statement Find the convergents to the fraction 57/44. Homework Equations Could anyone provide any good internet resuorces about "finding the convergents to the fraction"? The Attempt at a Solution

Homework Statement Obviously, we can make rockets to go very fast, but what is a reasonable top speed? Assume that a rocket is fired from rest at a space station in deep space, where gravity is negligible. If the rocket ejects gas at a relative speed of 1100 and you want the rocket's...

My algebra is really rusty, anyway I'm trying to simplify a Transfer Function so I have H(jw)=ZL/R+ZL so ZL is the impedance of an inductor and R is the impedance of the Resistor, my question is how would I go about simplifying that transfer function into it's simplest form? Thanks...

So I've been thinking about this problem for quite some time now any help will be appreciated. A sample of C_{2}H_{2}(g) has a pressure of 7.4 kPa. After some time a portion of it reacts to form {C}_6{H}_6 (g). The total pressure of the mixture of gases is then 3.6 kPa. Assume the volume and...

I'm looking at this particular splitting of a fraction in a book and I'm not completely sure what rule is being invoked. Here it is: http://www.apthtml.com/images/split.png Can anyone identify what this is?

Homework Statement \frac{(cos60 - isin60)^5 * (cos45 - isin45)^3}{(cos15-isin15)^7} Homework Equations The Attempt at a Solution I have had several tries so far, but simply do not know what to do. Would somebody be so kind and simplify this expression step by step. I...

Homework Statement What is f'(x) of f(x) 1/sqrt(2x)? 2. The attempt at a solution In applying the problem to the derivative formula: (1 / sqrt(2(x + h)) - 1 / sqrt(2x)) / h I multiplied the problem by a special form of one but that only put the rationals on the bottom of the...

Homework Statement I need to solve the following integral: { x * ((1-x)/3)^(1/7) dx where { represents the integral symbol b/c I don't know how to type that. The Attempt at a Solution I've tried integration by parts and don't get anywhere. None of the integration techiques I...

I am having trouble to find a straight forward method for finding coefficients using partial fraction expansion with repeated or complex roots. My study notes arent too clear so I am finding the differentiation method hard to follow for repeated roots. As for complex roots I can find the roots...

Hello, Is there any recommended reference for the subject "General Partial Fraction Exapnsion"? Thanks in advance

Homework Statement 1/[s*(s^2 + 4)] Homework Equations The Attempt at a Solution 1/[s*(s^2 + 4)] = A/(s) + (Bs + C)/(s^2 + 4) => 1 = A(s^2 + 4) + (Bs + C)s s = 0 1 = A(0 + 4) + (B*0 + C)*0 A = 1/4 s = i 1 = A(i^2 + 4) + (Bi + C)i 1 = A(i^2 + 4) + Bi^2 + Ci 1 =...

Homework Statement I just can't understand it I've read plenty of guides online, I just can't figure it out. How do you do partial fraction decomposition the farthest i can get is below 1/[(s^2 + 1)(s+1)] Homework Equations The Attempt at a Solution 1/[(s^2 + 1)(s+1)] = A/(s+1)...

Homework Statement If \lim_{z\rightarrow z_0}f(z)=A and \lim_{z\rightarrow z_0}g(z)=B then prove that \lim_{z\rightarrow z_0}\frac{f(z)}{g(z)}=\frac{A}{B} for B\neq0 The Attempt at a Solution I write f(z)=A+\epsilon_1(z) and g(z)=B+\epsilon_2(z), where the epsilon-functions tend to zero as z...

Homework Statement Show that the fraction of electrons within kT of the fermi level is equal to 3kT/2Ef, if D(E) = E^1/2. Homework Equations f(E) = 1 / ( exp(E-Ef)/kT + 1 ) fermi distribution N = integral from 0 to inf of D(E)f(E)dE = total no. of electrons The Attempt at a...

My TI 83 plus has a function called "Frac" which makes decimal numbers into fractions. If I have 0.33333... on the screen and press Frac the calculator returns 1/3. My question is how does this function work.

Derive the following equation for the fraction of a solute in layer 1 of the 2 layers formed by two immiscible liquids; Fraction of solute in layer 1 = (KD*V1)/((KD*V1)+V2) where KD=Distribution coefficient for the solute between chemical in V1 and chemical in V2 V1=Volume of liquid...

Homework Statement A small piece of aluminum(atomic number 13) contains 1015 . (The atomic number is the number of protons; it determines the (positive) electric charge of the nucleus and, thus, the number of electrons in a neutral atom.) If the piece of aluminum has a net positive charge of...

Find the area of the region under the graph of the function f on the interval [5, 10]. F(x) = 9/x

Homework Statement hey guys just wondering if anyone could help me simplify this. thansk [1-(y2/x2)]/[1+(y2/x2)] Homework Equations The Attempt at a Solution

I am just coming back to math after a, oh 30 year or so, vacation. In the class I'm taking, we are studying Partial Fraction Decomposition ( Px/Qx:Qx). It doesn't entirely make sense to me, tho like a monkey typing the great American novel, I can solve them given enough time. I am just having...

I am trying to find the integral of the following: \int\left({\frac{3 + 5x - 6x^2 - 7x^3}{2x^2}}\right)dx What I did was to split up the fraction like so: \int\left({\frac{3}{2x^2}}\right)dx + \int\left({\frac{5x}{2x^2}}\right)dx + \int\left({\frac{6x^2}{2x^2}}\right)dx +...

Hello, Is there a general form for the nth derivative for a fraction? Thanks in advance.

This might be a silly question: Is there a meaningful way to use L'Hospital's rule to determine \lim_{\vec{\mathbf{x}} \rightarrow \vec{\mathbf{0}}}\frac{x^3}{x^2+y^2}? where \vec{\mathbf{x}}=\left(\begin{array}{c}x\\y\end{array}\right)

3.741 (41 is recurring) answer is 1852/495 but ii don't know how to work it out thanks :)

Homework Statement It is a really long word problem, but I only need help with integrating one part of the proble. Homework Equations I need to know how to integrate 2+5sin((4*pi*x)/(25)) The Attempt at a Solution I tried using the chain rule by first integrating the sin into...

Homework Statement Find the partial fraction decomposition of : \frac{x^2}{(1-x^4)^2} The Attempt at a Solution \frac{x^2}{(1-x^4)^2}=\frac{A}{(1-x^4)}+\frac {B}{(1-x^4)^2} =A(1-x^4)+B when x=1 1=A(1-1^4)+B Hence B=1 and A=0 \frac{x^2}{(1-x^4)^2}=\frac{0}{(1-x^4)}+ \frac{1}{(1-x^4)^2}...

Homework Statement The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface. For an object with a coefficient of 0.59, what fraction of the object's kinetic energy is lost during a single...

Homework Statement do we look at the nominator or the denominator? are we trying to separate them? factoring them? thanks

I wasn't exactly sure where to put this, so I decided to try this section. It may be more appropriate to put this in the Calculus / Analysis section... I don't know. Can anybody tell me whether or not it's possible to find the value of the continued fraction 0 + 1 / (2 + 3 / (4 + 5 / (6 +...

Homework Statement I am just looking for a hint on which rule to follow first; what would you tell me if I already know how to deal with an ordinary complex fraction? I tried using x (and multiplied everything) as the LCD and got the wrong answer. [SIZE="6"] 3 - \frac...

Homework Statement a - \frac {a}{1-\frac{a}{1-a}} The Attempt at a Solution \frac{a}{1-a} This might be the part where I am confused. I always get confused when I need to factor out a -1 from this fraction's denominator in order to put it into the form of \frac{a}{a-1} So here...

Can anyone explain why \frac{-1}{x_0^2} (x - x_0) = \frac{-x}{x_0^2} + \frac{1}{x_0}? Is \frac{-1}{x_0^2} (x - x_0) = \frac{-1}{x_0^2} . \frac{(x - x_0)}{1}? After that I multiply to get \frac{-1}{x_0^2} (x - x_0) = \frac{-x + x_0}{x_0^2} = \frac{-x}{x_0^2} + \frac{x_0}{x_0^2}. Then divide...

Homework Statement x^3+1 / x^2+4 Homework Equations The Attempt at a Solution after using long division i get : x + -(4x-1) / (x^2+4) then using partial fraction : -4x-1 / x^2+4 = bx+c / x^2+4 then i am stuck because if what i have is correct then they both are the...

HELP! on Partial Fraction Decomposition Problem! - Heavy Side Technique I am doing a partial fraction decomposition problem for my calc 2 class. We use the Heavy Side Technique, but I will take help either way! \frac{2x-1}{x(x^2+1)^2} Thank you!

Homework Statement \int \frac{x^{2}}{x^{2}-1} Homework Equations The Attempt at a Solution I divide bottom into the top because the degree is the same and get... \int 1-\frac{1}{x^{2}+1} My question is, from here, do I have to recognize the tan^{-1} or is it also correct to...

I'm having some difficulty Solving this partial fraction: (3.84e7)/(s(s^2+6.4e4s+1.6e9))= (3.84e7)/(s(s-3.2e4+j2.4e4)(s-3.2e4-j2.4e4) how do u find the angle? I know the equation but I don't know how to find the B with it conjugate. eq: 2B/_theta but I don't know how to...

Homework Statement 3. Find the partial fraction expansions of the following polynomials a) 10/[(s^2)(s^2+6s+10)] The Attempt at a Solution I assume i should expan the polynomial in the form A/s^2+B/s+(Cs+D)/(s^2+6s+10) but i stuck at finding B. Maybe my expansion is just wrong .. :(

If you have a fraction, for example, \frac{1}{{1.0091532\times10^{-12}} + 1} Is there a simple way to convert it to a more easily calculated form, specifically, 1-x (where x is a very small number)

i am given this function and need to integrate it \frac{4x+7}{\sqrt{-4x^2+20x-9}} i have been trying to intergrate it by calling something T, preferably the expression under the sqrd root, or part thereof (-4x2+20x=T) but i can't find the way to do this, can't find the best expression that...

I'm having trouble finding the derivative of -2x^2+2x-7/x...I'm having trouble understand what to do with the X underneath. Do I bring X to the numerator and make it X^-1 or what? Thanks for your helphttps://www.youtube.com/watch?v=

Homework Statement Homework Equations No clue, honestly I'm trying to figure out what formula i need to use to start this problem. The Attempt at a Solution No clue, honestly I'm trying to figure out what formula i need to use to start this problem.

Homework Statement x3 - x2 - 5x / x2 -3x +2 Homework Equations The Attempt at a Solution Heres what I got 5/x-1 + 6/x-2 but if I multiply those 2 fractions together I do not get a cubic equation on top of the line. I learned how to do these questions with linear equations on...