Partial Definition and 1000 Threads

Write a partial sum for the power series, URGENT Consider the function ln(1+4x). Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were Sigma from n=0 to infinity of 3^nx^2n , you would write...

Hello. I have equation: \frac{\partial T}{\partial t}-\frac{1}{2}\cdot \frac{(\partial)^2 T}{\partial x^2}=0 I calculated determinant: \Delta=(-\frac{1}{2})^2)-4\cdot 1 \cdot 0 \Rightarrow \sqrt{\Delta}=\frac{1}{2} \\ (\frac{dT}{dt})_{1}=-\frac{1}{4} \\ (\frac{dT}{dt})_{2}=\frac{1}{4} next...

Homework Statement Demonstrate that C_{Y,N}=\left ( \frac{ \partial H}{\partial T } \right ) _{Y,N} where H is the enthalpy and Y is an intensive variable. Homework Equations (1) C_{Y,N}=\frac{T}{N} \left ( \frac{ \partial S}{\partial T } \right ) _{Y,N} (2) T= \left ( \frac{ \partial...

Homework Statement Okay, so here's the problem: (a) Let U be a universal set and suppose that X,Y\in U. Define a relation,\leq, on U by X\leq Y iff X\subseteq Y. Show that this relation is a partial order on U. (b) What problem occurs if we try to define this as a relation on the set...

Homework Statement I have this lowpass circuit which I have transformed to the S-domain. The circuit is to be exposed to a unit step, and then I shall convert the transient response to the time domain. Here's the transfer function of the lowpass circuit: H(s) = \frac{\frac{1}{LC}}{s^2 +...

As part of a project I have been working on I fin it necessary to manipulate the following expression. e^(icx)/(x^2 + a^2)^2 for a,c > 0 I would like to decomp it into the form A/(x^2 + a^2) + B/(x^2 + a^2) = e^(icx)/(x^2 + a^2)^2 but I am having trouble getting a usable outcome.

I'm have a little trouble understanding PA=LU, I have no problems with A=LU but can't seem to figure out the Permutation matrix. So I have summarised the process I am using let me know where it can be improved. Step 1: Using Gaussian Elimination with partial pivoting reduce A to form a...

Hi guys I have a question here relating integration by partial praction.. the question said what is the antiderivative of x^2+2x-1/2x^3 +3x^2 - 2x valid only when x > 1/2. anyway i had poor background in math and working hard to catch up... I don't understant why "valid only...

In partial fractions, why \frac{3x+5}{(1-2x)^2} = \frac{A}{(1-2x)^2} + \frac{B}{(1-2x)} and not \frac{3x+5}{(1-2x)^2} = \frac{A}{(1-2x)} + \frac{B}{(1-2x)} Why exists the exponent on the denominator in the right hand side of the equation?

Homework Statement Find functions y=y(x) defined on (-∞,0) or (0,+∞) which verify: xy'+(x2-1)cot(y)=0, y(x_0{})=y_0{} for x_0{}≠0 and cos(y_0{})≠0The Attempt at a Solution I'm really stuck on this one! Any help will be very much appreciated!

Homework Statement Hi. My first post! I'm trying to solve for where a is a constant: ∫ (x/a)1/2*(x/(x-a)) dx Homework Equations See above The Attempt at a Solution I've tried integration by parts by setting u=(x/a)1/2 but I end up having to solve ∫ (x/a)1/2ln(x-a) - which I...

For a function such as w=5xy/z How would you find the partial derivative of w with respect to y or z? I've tried using basic logarithmic differentiation, but can't arrive at the correct answer. For reference, the correct answer is wy=5*(xy/z/z)*ln(x)

1. In the Khan academy video I watched on partial derivatives, I understand absolutely everything except for the last 20 seconds which confused me. http://www.youtube.com/watch?v=1CMDS4-PKKQ Using the formula: Z = x² + xy + y² @z/@x = 2x +y x=0.2, y=0.3 2(.2) + .3 = .7 What...

Homework Statement (x,y) = x√(xy) The answer says: fx=3/2*√(xy) fy=(x√x) / (2√y) fxx= (3√y) / (4√x) fxy= (3√x) / (4√y) fyx =(3√x) / (4√y) fyy = -(x√x) / (4y√ I don't get from the beginning. shouldnt fx be equal to (3/2)x^2 * (x^3 * y)^-(3/2)?? When I do second derivative fxx from fx, it...

Homework Statement x^2-x-13/(x^2+7)(x-2) hello i am having trouble solving this problem.. could anyone please show me how to do this step by step? i know polynomial long division is required before it can be converted to partial fractions. I also know the answer is 2x+3/x^2+7 - 1/x-2...

Homework Statement I want to check the answer to this question. ⌠ 2 x dx / (x+1) (x+2) ⌡ 1 Homework Equations The Attempt at a Solution For partial fraction I got A= -1 and B = 2 My final answer is -ln 2 + ln4 - ln3 = ln 4/ ln2 * ln 3

Homework Statement Consider the following reaction: CH3OH(g) <-> CO(g)+2H2(g) Calculate ΔG for this reaction at 298 K under the following conditions: PCH3OH=0.895atm PCO=0.115atm PH2=0.200atm Homework Equations ΔG=-R*T*ln(K) where R is the gas constant 8.314 J/molK, T is 298 in...

Hi, I have the following PDE-S\frac{\partial\vartheta}{\partial\tau}+\frac{1}{2}\sigma^2\frac{X^2}{S}\frac{\partial^2\vartheta}{\partial\xi^{2}} + [\frac{S}{T} + (r-D)X]\frac{\partial\vartheta}{\partial\xi}I am asked to seek a solution of the form \vartheta=\alpha_1(\tau)\xi + \alpha_0(\tau)...

Homework Statement In one of the workings of a question I couldn't solve(from solution sheet) there was one step I couldn't understand. Homework Equations \frac{1}{x^2+x+1} = \frac{1-x}{1-x^3} The Attempt at a Solution Tried partial fractions(unfactorable denominator) and could'nt get it...

I have x=x(t) and y=y(t) and I'm working in polar co-ordinates so $$x=rcos{\theta}$$ and $$y=rsin{\theta}$$. I want to find ${\theta}'(t)$ so by the chain rule I want $${\theta}'(x)*x'(t)+{\theta}'(y)*y'(t)$$. I know $${\theta}=arctan(y/x)$$ but how do I partially differentiate theta w.r.t x and y?

We have a function f:R^2->R and it has partial derivative of 2nd order. Show that f_{xy}=0 \forall (x,y)\in \mathbb{R}^2 \Leftrightarrow f(x,y)=g(x)+h(y) The <= is self explanatory, the => I am not sure I got the right reasoning. I mean we know that from the above we have: f_x=F(x) (it's...

Homework Statement \frac{2e^3}{((s^2)-6s+9)*s^3} you can factorize the denominator into s,s,s,(s-3),(s-3) that gives you 5 residuals. the first 3 should all be the same value but that's apparently not correct, so where am I going wrong?

Homework Statement given z=yf(x^2-y^2) show that the x(∂z/∂y)+y(∂z/∂x)=xz/y The Attempt at a Solution cut it short, my ∂z/∂y= f(x^2-y^2)-2(y^2)f(x^2-y^2) ∂z/∂x=2xyf(x^2-y^2) i was able to prove that x(∂z/∂y)+y(∂z/∂x)=xz/y But i need help with partial differentiations...

Homework Statement I'm supposed to decompose 1 / x(x2 + 1)2 Also, we haven't learned matrices yet so I can't use that technique to solve it. Homework Equations None. The Attempt at a Solution 1 / x(x2 + 1)2 = A/x + (Bx + C) / (x2 + 1) + (Dx + E) / (x2 + 1)2 I multiplied...

Homework Statement Find the partial derivatives: f(x,y)= integral[x,y] cos(t^2)dt, find f_x(x,y) and f_y(x,y) Homework Equations I know from calculus that the derivative of an integral is the function. The Attempt at a Solution I found that the integral of [x to y]...

Homework Statement The electric potential in a certain region of space is given by: V(x,y,z) = 1000x-2000y-1500z(Volts). a.)Find the electric field corresponding to the given electric potential. Draw some electric field lines. b.) What charge distribution can create this electric field? Give...

urgent reply needed Can we use partial means as a predictor for the response while fitting a regression line or curve?.

Homework Statement Inverse Fourier of: [ jω+2 ] / [ (jω)2 +5jω+9 ] where j = sqrt(-1) I tried using partial fractions but the denominator can't be factored...I tried completing the square on the denominator but I get a sum of squares. What can I try? I am sure I don't have to use the formal...

Homework Statement ∫(x3+4)/(x2+4)dx Homework Equations n/a The Attempt at a Solution I know I have to do long division before I can break this one up into partial fractions. So I x3+4 by x2+4 and got x with a remainder of -4x+4 to be written as x+(4-4x/x2+4). Then I rewrote...

Homework Statement The question is attached along with its solution. Homework Equations Partial differentiation and the implicit function theorem. The Attempt at a Solution My work is attached. I feel it's correct but is it incomplete? I have the following questions/confusions...

When you have waves that are out of phase by some fraction of a cycle, e.g not exactly in phase and not exactly 180 degrees anti-phase, how do you determine the phase (relative to the original component waveforms) of the resultant? Specifically, is there an equation that solves for phase...

Hi, I find my professor doing this a lot of times, here is it: ∫{ ∂(f[x])/∂x } dx = ∫d(f[x]) How is that possible?

Homework Statement Given 4 state variables x, y, z and w such that F(x,y,z)=0 and w depends on 2 of the other variables, show the following relations: 1)\left ( \frac{\partial x }{\partial y } \right ) _z = \frac{1}{\left ( \frac{\partial y }{\partial x } \right ) _z} 2)\left (...

Can this be done? If so, how can I go about doing so? This is merely a potential science fair idea for 2013.

Homework Statement We were given a worksheet to integrate some problems using partial fractions. This one however I cannot figure out what to do with it. This is the problem. ∫(x3-4x2+x+6)/(x2-x+2) dx The Attempt at a Solution using long division i got ∫(x-3) (-4(x-3)/(x2-x+2) dx...

Homework Statement w = 2xy + 4yz + 5xz x = st y = 3^(st) z = t^2 s=5 t=1 Homework Equations Chain rule: xy = x*y' + y*x' The Attempt at a Solution w = 2stest + 4test + 5st3 (partial derivatives) dw/dt = 2s2test + 2sest + 4tsst + 4est + 15st2 (partial derivatives) dw/dt (5,1) = 2(5)2e5 +...

$$ \frac{1}{z^2(1-z)} = \frac{A}{z^2}+\frac{B}{1-z} $$I can't figure out how to decompose this fraction.

Homework Statement In the steps below, the ∂z/∂x does not seem to be obeying normal algebraic rules. I'm confused. This is not really a problem, I'm just trying to understand the steps. The Attempt at a Solution 1. 3z2∂z/∂x - y + y∂z/∂x = 0 2. ∂z/∂x = y/(y + 3z2) if ∂z/∂x were...

If you have a function f(x,y)=xy where y is a function of x, say y=x^2 then the partial derivative of f with respect to x is \frac{\partial f}{\partial x}=y However, if you substitute in y and express f as f(x)=x^3 then the partial derivative is \frac{\partial...

Homework Statement The question is attached as Question.jpg. Homework Equations Partial differentiation. The Attempt at a Solution This seems obvious to me but I don't know how to express myself mathematically. Basically, what I'd do is: [∂(u,v)/∂(x,y)] [∂(x,y)/∂(r,s)] =...

Homework Statement ∂f/∂x (xy -1)2 = 2y(xy-1) The Attempt at a Solution I would think the answer would be 2(xy-1) I don't understand where the y comes from in 2y

Homework Statement If f is a quadratic function such that f(0) = 1 and \int \frac{f(x)}{x^2(x+1)^3}dx is a rational function, find the value of f '(0). Homework Equations The Attempt at a Solution This question is presented in the context of learning about integration by...

Homework Statement I don't understand why ∂f/∂x = xy = y whereas ∂f/∂x = x2 + y2 = 2x Why does the y disappear in the second but not in the first?

So I don't understand why if you have something like U(x,y) = f(y+2x) and you take \frac{\partial U}{\partial x} = \frac{\partial f}{\partial x} you get \frac{df}{d(y+2x)} * \frac{d(y+2x)}{dx} Why does the partial derivative just change to the total derivative for one variable? It...

Homework Statement I can't seem to find information on this specific question i have. So I'm taking the partial derivative of this equation for both x and y I know how to do it for y, but I am not seeing something with respect to x fx(x,y)= x^7 + 2^y + x^y Homework Equations The Attempt at...

Hi everyone: How is the following derived? Just for example: \Deltax\alphae\alpha=\Deltax\alpha(\delta/\deltax\alpha) does it not mean? e\alpha=\delta/\deltax\alpha But How?

Have worked through to get some sort of answer, but find the evaluation (simplest bit) impossible - wood for trees, I think. given d2(e^(xy^2)/dy^2 I need to evaluate for x=2, y=0 now using chain rule d(e^(xy^2))/dy = d(e^u)/du du/dy where u=xy^2 & d(e^u)/du = e^u => x(2y) e^(xy^2) fine...

Homework Statement This is the first problem of the two. Homework Equations The Attempt at a Solution Using separation of variables, I end up with T'(t)= -λKT(t) and X''(x)+(β/K)X'(x)/X(x)= -λ. At first I chose the negative lambda because I saw that U(0,t) and U(L,t) needed to oscillate...

Homework Statement I have the series 1^3+2^3+3^3...n^3, and need to find a formula containing n to represent the sum of the nth terms. The motivation is to find a conjecture, which I can then prove using mathematical induction. The Attempt at a Solution I see that n=1 , 1^3=1...

Homework Statement Suppose the function f:R^2→R has 1st order partial derivatives and that δf(x,y)/δx = δf(x,y)/δy = 0 for all (x,y) in R^2. Prove that f is constant; there exists c such that f(x,y) = c for all (x,y) in R. There's a hint as well: First show that the restriction of...