Partial Definition and 1000 Threads

Homework Statement 1/ (x+8)(x^2+16) Find the integral Homework Equations I keep getting this question wrong. Can someone check my steps? The Attempt at a Solution I set it up as A/(x+8) + (Bx+C)/(x^2+16) So I did, A(x^2+16)+ (Bx+C)(x+8) and I did that and got A+b=0...

Homework Statement (2x^3-2x+1)/(x^2/3x) Find the integral. 2. The attempt at a solution So I've been on this problem for like an hour now and I don't know what I'm doing wrong. So I used long division and got 2x+ (4x+1)/(x^2-3x) ∫2x + ∫(4x+1)/(x^2-3x) = x^2 +...

Homework Statement I(alpha) = ∫1/((x+alpha^2)(x+1)) dx between the limits of 0 and infinity Evaluate the integral above depending on the parameter alpha using partial fractions. The Attempt at a Solution 1/((x+alpha^2)(x+1)) = A/(x+alpha^2) + B/(x+1) 1 = A(x+1) + B(x+alpha^2)...

I am trying to separate out \[ \frac{s}{(s+1)^3} \] for an inverse Laplace transform. How does one setup up partial fractions for a cubic? I know for a square I would do \[ \frac{A}{s+1} + \frac{Bs+C}{(s+1)^2} \] I tried doing \[ \frac{A+Bs}{(s+1)^2} + \frac{Cs^2+Ds+E}{(s+1)^3} \] which led to...

Homework Statement ∫(5x2+20x+6)/(x3+2x2+x Homework Equations The Attempt at a Solution (5x2+20x+6)/(x3+(x(x2+2x+1) (5x2+20x+6)=(A/x)+(B/(x+1))+(C/(x+1)) (5x2+20x+6)=x2(A+B+C)+x(2A+B+C)+A 5=A+B+C 20=2A+B+C 6=A It's not coming out quite right. Did I maybe factor the...

Homework Statement ∫(2x3-4x-8)/(x2-x)(x2+4) dx Homework Equations The Attempt at a Solution ∫(2x3-4x-8)/x(x-1)(x2+4) dx Next I left off the integral sign so I could do the partial fractions: 2x3-4x-8=(A/x)+(B/(x-1))+((Cx+D)/(x2+4))...

Homework Statement Use integration by parts to evaluate the integral ∫(7-6x) / (x2-4x+13)The Attempt at a Solution This is a question from my notes so I already have the solution but I'm not sure what's going on at this one specific step. ∫(7-6x) / (x2-4x+13) = -∫(6x-7) / (x2-4x+13) = -∫(...

Homework Statement If ##xs^2 + yt^2 = 1## (1) and ##x^2s + y^2t = xy - 4,## (2) find ##\frac{\partial x}{\partial s}, \frac{\partial x}{\partial t}, \frac{\partial y}{\partial s}, \frac{\partial y}{\partial t}## at ##(x,y,s,t) = (1,-3,2,-1)##. Homework Equations Pretty much those just listed...

Use integration to find a solution involving one or more arbirary functions \frac{\partial u}{\partial y}=\frac{x}{\sqrt{1+y^2}} for a function u(x,y,z) u(x,y,z)=x\int \frac{dy}{\sqrt{1+y^2}} let y=\sinh v u(x,y,z)=x\int \frac{\cosh v\: dv}{\sqrt{1+\sinh ^2v}} u(x,y,z)=x\sinh ^{-1}y+f(x,z)...

Ok I'm stuck I have \int \frac{x^2 - 5x + 16}{(2x + 1)(x - 2)^2} \, dx and I got to this part: x^2 - 5x + 16 = A(x - 2)^2 + B(x - 2)(x + \frac{1}{2}) + c(x + \frac{1}{2})So do i need to distribute all of these and factor out or is there a simpler way? I found a solution where they are just...

Hello, first post here. Here is a hypothetical partial pressure of gas question Imagine you have a two component system: Component 1 is water Component 2 is an imaginary substance that is immiscible with water, but has same boiling temp / pressure You put the two components in a...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Hello MHB members and friends!(Callme) An economy student asked me, if I could explain the following partial differentiation: \[\frac{\partial}{\partial C(i)}\int_{i\in[0;1]}[C(i)]^\frac{\eta - 1}{\eta}di =\int_{j\in[0;1]}[C(j)]^\frac{\eta - 1}{\eta}dj\frac{\eta -...

Quick question... I know that if the numerator is greater than the denominator I need to divide out by long division BUT If the numerator is equal to the denominator (the exponent is what I'm talking about to be specific) then, do I need to do anything? Because I'm stuck on this problem \int...

Homework Statement (t4+9)/(t4+9t2) Homework Equations The Attempt at a Solution I'm not completely sure if I'm using the correct method to solve this. Since the degrees of the numerator and denominator are the same, wouldn't you divide the denominator into the numerator? Here is...

Homework Statement A function f(x,t) depends on position x and time t independent variables. And if \dot{f} represents \frac{df(x,t)}{dt} and \dot{x} represents \frac{dx}{dt}, then find the value of \frac{\partial\dot{f}}{\partial\dot{x}}. Homework Equations The Attempt at...

So figuratively, I'm trying to win a nuclear war with a stick. :smile: I did not take any course in PDEs, I just self-studied some of them, and now I'm toast. :smile: First, please feel free to hurl rocks at me if my simplification is incorrect...

Homework Statement Solve the inhomogenous partial differential equation \frac{∂^{2}u}{∂t^{2}}-\frac{∂^{2}u}{∂x^{2}}=-6u^{5}+(8+4ε)u^3-(2+4ε)u by using the NDSolve function in Mathematica for the interval [0,10] x [-5,5]. Homework Equations Initial conditions: u(0,x)= tanh(x)...

Q3.) Express as partial fractions. a) \frac{3x+4}{x^2+3x+2} b) \frac{5x^2+5x+8}{(x+2)\left(x^2+2 \right)} c) \frac{x^2+15x+21}{(x+2)^2(x-3)}

Homework Statement Find an equation for the path of a particle that starts at P(10,10) and always moves in the direction of maximum temperature increase if the temperature in the plane is T(x,y) = 400-2x^2 -y^2 Homework Equations T(x,y) = 400-2x^2 -y^2 dT/dx = -4x dT/dy = -2y...

Here is the question: I have posted a link there so the OP can view my work.

http://en.wikipedia.org/wiki/Partial_fraction_decomposition In general, if you have a proper rational function, then: if ## R(x) = \frac {P(x)}{Q(x)} ## and ## Q(x) = (mx + b)^n ... (ax^2 + bx + c)^p ## where ##Q(x)## is composed of distinct linear powers and/or distinct irreducible...

Homework Statement Show that a relation of the kind ƒ(x,y,z) = 0 then implies the relation (∂x/∂y)_z (∂y/∂z)_x (∂z/∂x)_y = -1 Homework Equations f(x,y) df = (∂f/∂x)_y dx + (∂f/∂y)_x dy The Attempt at a Solution I expressed x = x(y,z) and y = y(x,z) then found dx and...

Hello all, I am trying to calculate the second order of the partial derivative by x of the function: f(x,y)=(x^2)*tan(xy) In the attach images you can see my work. Both the answer in the book where it came from and maple say that the answer is almost correct, but not entirely. In the last...

Homework Statement I'm taking the Laplace transform of F(s), and the first thing is to expand it by partial fraction or something so that I can match F(s) with a table of laplace transforms. Homework Equations The Attempt at a Solution Does partial fraction even work? I've got two...

Ok folks, I've taken a stab at the Latex thing (for the first time, so please bear with me). I've mentioned before that I'm teaching myself relativity and tensors, and I've come across a question. I have a few different books that I'm referencing, and I've seen them present the ordinary...

Homework Statement z = x^2 +y^2 x = rcosθ y = rsinθ find partial z over partial x at constant theta Homework Equations z = x^2 +y^2 x = rcosθ y = rsinθ The Attempt at a Solution z = 1 + r^2(sinθ)^2 dz/dx = dz/dr . dr/dx = 2(sinθ)^2r/cosθ = 2tanθ^2x...

Hi everyone! I'm not sure if this is the right forum to post my question. If I'm wrong, let me know it. The question: Let us consider the functions \theta=\theta(x,y), and M=M(\theta), where M is a operator, but i doesn't relevant to the problem. I need to know the derivative \frac{\partial...

Homework Statement Well this is part of an integration process, namely: \int \frac {sin^2x}{4+3cos^2x}dx Homework Equations My attempt involved using a u-substitution, namely t = tan x The Attempt at a Solution Using t = tan x, sin^2 x = \frac {t^2}{1+t^2} and cos^2 x = \frac...

Is there a derivation for ∂f(x,y)/∂x given: f(x,y): g(x,y)h(x,y) e.g. sin(x)(x+2y)

Homework Statement Hi Say I have a function f(x(t), t). I am not 100% sure of the difference between \frac{df}{dt} and \frac{\partial f}{\partial t} Is it correct that the relation between these two is (from the chain rule) \frac{df}{dt} = \frac{\partial f}{\partial t} +...

Hello there, This isn't specifically homework, it is study. I'm having a difficult time trying to understand how to calculate/estimate partial decay widths, \Gamma[\itex], and Branching Ratios. I haven't found very clear information online so far. Here's just an example below that I'd like...

Homework Statement let V=f(x²+y²) , show that x(∂V/∂y) - y(∂V/∂x) = 0 Homework Equations The Attempt at a Solution V=f(x²+y²) ; V=f(x)² + f(y)² ∂V/∂x = 2[f(x)]f'(x) + [0] ∂V/∂y = 2[f(y)]f'(y) I'm sure I've gone wrong somewhere, I have never seen functions like this...

Homework Statement Suppose we have a mixture of the gases H2, CO2, CO and, H2O at 1200 K, with partial pressures pH2 = 0.55 bar, pCO2 = 0.2 bar, pCO = 1.25 bar, and pH2O = 0.1 bar. Is the reaction described by the equation CO + H2O <=> H2 + CO2 at equilibrium under these conditions? If not...

For spherical coordinates, u(r,\theta,\phi) is function of r,\theta,\phi. a is constant and is the radius of the spherical region. Is: \int_{0}^{2\pi}\int_{0}^{\pi}\frac{\partial\;u(r,\theta,\phi)}{\partial {r}}a^2\sin\theta d\theta d\phi=\frac{\partial}{\partial...

Hello, I am not completely certain why in thermodynamics, it seems that everything is done as a partial derivative, and I am wondering why? My guess is because it seems like variables are always being held constant when taking derivatives of certain things, but it is still somewhat a mystery to...

Hi I have a question about partial derivatives? For example if I have a function x = r cos theta for all functions, not just for this function will dx/d theta be the inverse of dtheta/dx, so 1 divided by dx/d theta will be d theta/ dx? Please help on this partial derivative question...

I got x = (u2 - v2) / u y = (v2 - u2) / v I differentiated them w.r.t u & v respectively & solved the given equation but I'm not getting the answer which is 0. Please view attachment for question!

Homework Statement let u=f(x,y) , x=x(s,t), y=y(s,t) and u,x,y##\in C^2## find: ##\frac{\partial^2u}{\partial s^2}, \frac{\partial^2u}{\partial t^2}, \frac{\partial^2u}{\partial t \partial s}## as a function of the partial derivatives of f. i'm not sure I'm using the chain rules...

I was working on a pde, and I needed to compute a Jacobian for it. Suppose we have a function consisting of a series of matrices multiplied by a vector: f(X) = A * B * b --where X is a vector containing elements that are contained within A, b, and/or b, --A is a matrix, B is a matrix, and b is...

I was working on PDE for a project and needed to compute a Jacobian for it. Suppose we have a function consisting of a series of matrices multiplied by a vector: f(X) = A * B * b --where X is a vector containing elements that are contained within A, b, and/or b, --A is a matrix, B is a...

Here are the questions: I have posted a link there to this thread so the OP can see my work.

Se a function f(x(t, s), y(t, s)) have as derivative with respect to t: \frac{df}{dt}=\frac{df}{dx} \frac{dx}{dt}+\frac{df}{dy} \frac{dy}{dt} And, with respect to s: \frac{df}{ds}=\frac{df}{dx} \frac{dx}{ds}+\frac{df}{dy} \frac{dy}{ds} But, how will be the derivative with respect to...

Homework Statement If you sum this from one to infinity. Ʃ (cos(1/(n)^2 - cos(1/(n+1)^2) Homework Equations The Attempt at a Solution Ʃ (cos(1/(n-1)^2 - cos(1/(n+1)^2) This is telescoping if you work that out for the partial nth partial sum you get cos(1) -...

Homework Statement http://i.minus.com/jbzyIAyMvUrADW.png Homework Equations Conservation of mass in a closed system. The Attempt at a Solution I'm not sure what the lecture is getting at here. Why is it that the number of moles of NO2 added to twice the number of moles of N2O4...

Homework Statement ∫▒√(1+x^2 )/x dx Homework Equations The Attempt at a Solution I don't know how to break this up. I know we break partial fraction problems up based on their denominator, however the denominator i this problem is just 'x'.

Homework Statement A mixture of He, Ne, and Ar has a total pressure of 0.80 atm and is found to contain 0.55 mol He, 0.94 mol Ne, and 0.35 mol Ar. What is the partial pressure of each gas in atm? Homework Equations Partial pressure for a gas is equal to the mole fraction of the gas...

Hello Everyone, So in other words, if you didn't understand what I'm saying from the title of this post, look at it this way: What is the answer to this integral? ∫(partial dx)/(partial dt) * dx According to my textbook the answer is 0 but I'm getting easily confused as to how this is...

Hello everyone, I have read about the theoretical values of the Z boson decay partial width and how well they agreed with experiment. However there is something I do not quite understand: since these theoretical calculations were performed with the hypothesis that the masses of the decay...

Given a function: z(x,y) = 2x +2y^2 Determine ∂x/∂y [the partial differentiation of x with respect to y], Method 1: x = (z/2) - y^2 ∂x/∂y = -2y Method 2: ∂z/∂x = 2 ∂z/∂y = 4y ∂x/∂y = ∂x/∂z X ∂z/∂y = (1/2) X 4y = 2y One or both of these is wrong. Can someone point out...