Expression Definition and 999 Threads

Determine an expression for f(x) =(1+x)(1+2x)(1+3x)…(1 +nx),find f⸍(0) .

Homework Statement http://sites.math.rutgers.edu/~ds965/temp.pdf (NUMBER 2)[/B]Homework Equations I do not understand the alternating part for the second problem and the recursive part for the first problem.The Attempt at a Solution The first answer I got was first by writing out the...

Homework Statement Homework Equations 3. Solution Then the equations from part (A) are used--but why does the converted trig (1-cos(etc)) go away? Does this have to do with the mean-squared bit?

Homework Statement Homework EquationsThe Attempt at a Solution U = 5x2 - 20x F = -dU/dx F = -10x + 20 The expression for force doesn't look like motion is SHM . How should I deal with this ?

Hello everyone ! I've started to work on integral and I wonder if it's possible to calculate the expression of the antiderivative with the expression of the "integrand"1 rather than use a table with the function and its antiderivative. Thank you in advance ! 1( I'm french and I d'ont know the...

Homework Statement [/B] I have this expression: dV/dt = F0 - K*h^(1/2); it describes a variation in time of a fluid volume V in a cone-shaped tank of total volume H*pi*R²/3; By a trigonometric relation we get V = (pi*R²/3*H²)*h³; since tan a = H/R = h/r where: R = radius of the tank; H =...

Homework Statement Hello there are two types of pens expensive and cheap. The ratio of the prices of the two is 3:7 The total cost for 30 of the cheaper pens and 10 of the expensive pens is $1568. I am asked to derive an expression for the cost of ONE of the expensive pens which i will...

Homework Statement My solution, is this correct? This is what I came up with. Y=A+((A*B)+B+C'+(B+C'*D)+D) Is it safe to say that it is correct or did I make a mistake?

1. Homework Statement Hi, I have done part a) by using the expression given for the lie derivative of a vector field and noting that if ##w## is a vector field then so is ##wf## and that was fine. In order to do part b) I need to use the expression given in the question but looking at a...

I was wondering whether it can ever happen that only a certain "length" of the same gene gets expressed in different species? Or perhaps even within the same species? (Without it being a random mutation) Basically, can a part of a gene be expressed, and still have some functionality in the...

Homework Statement Just a simple problem, I need to take the expression##\frac 1 2 (sin(2x)+1)## and show it is equivalent to ##sin^2(x+\frac \pi 4)##, and I can't seem to manage to find the way to do so, so I would appreciate some insight. Homework Equations N/A The Attempt at a Solution...

Homework Statement The question is Derive an expression for the closed loop gain of the differential amplifier. I have solutions for these questions but the solution for this question is quite vague. Here is the solution: I understand part 1 and part 3, but part 2 I don't. So looking at...

Homework Statement [/B] A solid sphere of mass M and radius R is suspended from a thin rod. The sphere can swing back and forth at the bottom of the rod. Find an expression for the frequency of small angle oscillations.Homework Equations f = 1/2(pi) sqrt(MgR/I) I for a solid sphere 2/5MR^2The...

Homework Statement I have to prove that the expression $$\frac{\omega C - \frac{1}{\omega L}}{\omega C - \frac{1}{\omega L} + \omega L - \frac{1}{\omega C}}$$ is equal to $$\frac{1}{3-( (\frac{\omega_r}{\omega})^2 + (\frac{\omega}{\omega_r})^2)}$$ where ##\omega_r= \frac{1}{\sqrt{LC}}##...

Hi All I am trying to simplify an algebraic expression, I know what the expression should simplify to but I am struggling to simplify it. The expression is: 2(2u+v)/u = 4(v^2-4u^2)/3u^2 and it is supposed to simplify to: 3u = 2(v-2u) I have approached this...

problem statement: need to show: ||w||_p^2+||u||_p^2-2(||u||_p^p)^{\frac{2}{p}-1}\Sigma_i(u(i)^{p-1}w(i)) can be bounded as a function of ||w-u||_p^2 where p\in[2,\infty) work done: the expressions are equal for p=2, and i suspect that...

Homework Statement 14.6 The coefficient of kinetic friction between the slider and the rod is μ, and the free length of the spring is ##L_0 = b##. Derive the expression for the work done by the friction force on the slider as it moves from A to B. Neglect the weight of the slider. Homework...

Homework Statement Derive the expression for the work done by the ideal spring on the slider when the slider moves from A to B. Assume that the free length of the spring is (a) ##L_0 = b##; and (b) ##L_0 = 0.75b## Homework EquationsThe Attempt at a Solution Can you check if my solution...

What exactly does it mean to simplify an expression. I understand that an expression becomes more simple when you combine like terms but what other conditions are there? Is x(5x+1) more or less simple than 5x^2 +x? Do square roots need to be moved to the numerator?

Homework Statement After a switch is left for a for many time constants, it is switched to b. find an expression for the total charge that passes through the resistor in one time constant Homework Equations dq/dt = I(t) I(t) = (ε/R)(e^(-tR/l)) The Attempt at a Solution so dq = I(t) dt I know...

Can someone help with the issue/problem of placing a superscript before a variable or expression ... as Just and Weese do in their book on Set Theory ... in the expression for a Cartesian Product as follows: Hope that someone can help ... Peter

How can I collapse macroscopic absorption cross-section of 4 groups into two ? Assuming that the first two groups are fast groups and the other twos are thermal . I am suffering with the following : 1- Do I have to assume that the groups are directly coupled ? 2-Does what apply on the two...

For those experienced with this stuff, Weinberg argues (Weinberg, QFT, Volume 1) that an expression for the anihilation operator acting on a state vector when all particles are either all bosons or all fermions is $$a(q) \Phi_{q_1 q_2 ... q_N} = \sum_{r=1}^{N} ( \pm 1)^{r+1} \delta (q - q_r)...

Given that $\alpha$ and $\beta$ are the roots of a quadratic equation, evaluate $\frac{1}{\alpha^2}+\frac{1}{\beta^2}$. I find this question to be interesting.

Homework Statement For the expression: $$E=\frac{E_{0}}{2}\left(\exp\left[\frac{j\pi V}{2V_{\pi}}\right]+j\exp\left[-\frac{j\pi V}{2V_{\pi}}\right]\right)$$ I want to show that if ##V=m(t)-\frac{V_{\pi}}{2}##, then ##|E|^2## can be written as...

Does anyone know of a general expression for the unit dyadic, given in terms of the language of general curvilinear coordinate systems?Perhaps an expression for its components?Perhaps an expression, just appropriate for use with orthogonal coordinate systems?$$~$$ In cartesian coordinates the...

Hello all. I am wondering why we raise the concentration to the exponent of the stochiometric coefficient. I understand why we take the products of reactants or products. For instance, let me give an example to show where I am getting mixed up. Let's say 2A +3B = 8C as a reversible...

Homework Statement I have derived the expression for the velocity of the satellite v= root of GM/r however I'm struggling to derive an expression for the centripetal acceleration of a satellite orbiting Earth. Homework EquationsThe Attempt at a Solution I'm not entirely sure which equations to...

Hi there, I'm hoping somebody can help me. I have to evaluate the following expression using BIDMAS rules without using a calculator: 1-2/32 I can get as far as 1-2/9 but the answer is 7/9. I don't understand how to get from 1-2/9 to 7/9 in my head. For instance 2/9 = 0.2 recurring, but...

1. The problem statement, all variables, and given/known data Homework Equations The Attempt at a Solution So basically I took vertical direction formula and I solved for "t". I then took the horizontal direction formula and solved for "x" or we can also call x the "Range" since that's...

Homework Statement Basic projectile motion if you throw from ground level, to obtain a max distance in the x you'd want to throw at a 45° angle right? So as your initial height increases, your throwing angle will decrease and my guess is as your initial velocity increases your angle increases...

Evaluate: \[\lim_{x\rightarrow 0}\frac{\sin (\arctan x)-\tan (\arcsin x)}{\arcsin (\tan x)-\arctan (\sin x)}\]

Show, that $$\tan^2 18^{\circ} \cdot \tan^254^{\circ} \in \Bbb{Q}.$$

Homework Statement Homework Equations $$(x-a)(x+a)=x^2-a^2$$ The Attempt at a Solution I have to express ##~\displaystyle x^2+16=f\left( \frac{x}{x-1} \right)## I guess it has to be ##~\displaystyle \left( \frac{x}{x-1} \right)^n-a~## or ##~\displaystyle \left( \frac{x}{x-1} \pm a...

Homework Statement I need help finding the appropriate expression to use to add a "new calculated column" to produce a vertical velocity vs time graph in Logger Pro. The lab consisted of a ball tied to a rope, creating a pendulum. The Go! Motion sensor was set up to record the oscillations. The...

I´m having a problem with the value of the expression ##F(it)-F(-it)##, found on the Abel-Plana formula, where $$F(z)=\sqrt{z^2 + A^2}$$, with ##A## being a positive real number (F(z) is analytic in the right half-plane). Well, I know the result is ##F(it)-F(-it)=2i\sqrt{t^2 -A^2}##, for...

I would like to know what the "0-ket", called vacuum state and used in the following expression, represents $$\Psi(x,t) = \int d^3x <x| \ a^{\dagger}(x) \ |0>$$ I have rewritten the expression for the case of just one ##x##. The expression above is usually presented with ##(x_1,...x_n)## (n...

Hello. I want to be able to create any mathematical equation or expression. So, one thing I want to confirm is that, to create any complex equation or expression, I should make use of Order of Operation - PEDMAS or BODMAS. Correct? The Order of Operation governs the result, and the Order of...

Factor the expression. x^4 - 15x^2 + 9 Let u = x^2 Let x^4 = (x^2)^2 u^2 - 15u + 9 Must I use the quadratic formula here or completing the square?

Factor. x^4 + 2x^2*y^2 + y^4 Must I change x^4 to (x^2)^2 and y^4 to (y^2)^2? Let u = x^2 Let v = y^2 (u)^2 + 2uv + (v)^2 Where do I go from here?

Factor (ax + b)^(-1/2) - [sqrt{ax + b}]/b This one is tricky. Can someone get me started?

Factor (x^3/8) - (512/x^3). LCD = 8x^3 (x^6 - 8(512))/8x^3 (x^6 - 4096)/8x^3 [(x^3 - 64)(x^3 + 64)]/8x^3 In the numerator, the expression (x^3 - 64) is the difference of cubes, right?

Factor [(a + b)^2]/4 - [a^2b^2]/9 Can someone get me started?

I am trying to prove that $$ x^4+4096y^4+450x^2y^2-2304xy^3-36x^3y $$ is positive for all positive $x$ and $y$. I also have the condition $x>16y$ though I don't believe this is needed to prove positivity as I've plotted the function for varying $x$ and $y$ and it always seems to be positive...

Homework Statement The directed beam from a small but powerful searchlight placed on the ground tracks a small plane flying horizontally at a fixed height h above the ground with a uniform velocity v. If the search light starts rotating with an instantaneous angular velocity ##\omega_0## at...

Precalculus by David Cohen, 3rd Edition Chapter 1, Section 1.3. Question 32c. Factor the expression. 3(x + h)^4 - 48(x + h)^2 Solution: Factor out 3(x + h)^2. 3(x + h)^2[(x + h)^2 - 16] Simplify the quantity in the brackets. 3(x + h)^2[(x + h) - 4][(x - h) + 4] Is this right?

Precalculus by David Cohen, 3rd Edition Chapter 1, Section 1.3. Question 29c. Factor the expression. 4a^2b^2 - 9(ab + c)^2 Must I expand the quantity (ab + c) before factoring?

]Homework Statement Solving the cubic equation x^3 + 6x = 20 by using formula gives (10+ sqrt(108))^1/3 - (-10 + sqrt(108))^1/3 How do you show that this comes out exactly 2? No calculators allowed.Homework EquationsThe Attempt at a Solution Tried cubing the expression and tried using the...

Homework Statement We are given Z, and are asked to find the magnitude of the expression. See attached picture(s) Homework Equations See attached pictures(s) The Attempt at a Solution When I solved it on the exam, I did it the long way using De Moivre's theorem. I ended up making a few sign...

Hey everybody,, I have question related to the expression of the maximally entangled state.. I know that that for W-state its given by ( For three qubits) : psi=(|100>+|010>+|001>)/sqrt(N) and for Disentangled state ( for three qubits) its given as : psi=|111> Where one and 0 represent the...