Root Definition and 918 Threads

Hello. How do I find the limit of this term? $$\lim_{{n}\to{\infty}}|\left(\frac{n}{n+1}\right)^{\!{n^2}}|^\frac{1}{n}$$

Hello. How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.

Hello. How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.

Here it is, for you to critique. This is a proof by contradiction. This is a good example of how I usually go about doing proofs, so if you give me tips on how to improve this particular proof, I'll be able to improve all my other proofs. I just learned how to do proof by contradiction...

for about first 429407636 pi digits where can i get such software or how can i calculate it? (i have 1b pi digits)

Goood Day, I have a cubic root equation. I use Newton-raphson for finding the roots. I want to do parameter estimation (tuning of the equation parameters to be able to give better prediction) using experiment data. Can anyone help me on how to do this? Thanks for your anticipated help...

I want compute the following integral: $$\\ \int f(x,y) \sqrt{dx^2+dy^2}$$ Is correct this pass-by-pass: $$\\ \sqrt{\left( \int f(x,y) \right)^2} \sqrt{dx^2+dy^2} = \sqrt{\left( \int f(x,y) \right)^2 (dx^2+dy^2)} = \sqrt{\left( \int f(x,y) \right)^2 dx^2 + \left( \int f(x,y) \right)^2 dy^2}...

I have attached a copy of a vector question which i cannot do, i do not even understand what the question is asking can someone help? On a different note i seem to have a lot of trouble with simplifying square roots for example what is the square root of 2704/ is there any way to find the...

The root locus design method is used to locate poles at desired locations. However, it is not possible to locate poles arbitrarily. Provide reasons for this statement. K = 1/│G(s)H(s)│ K G(s)H(s) = (2k+1)π I've formulated the answer for this as, The root locus gives the path of...

HelloI am trying to prove that if $c > 1$, then $c^{1/n} > 1$ , where $n\in \mathbb{N}$. Now I present my proof here. Since $c>1$, it follows that $c > 0$. Now $n^{\mbox{th}}$ root theorem says that if $a>0$,then there exists a unique positive $n^{\mbox{th}}$ root of $a$. So $c^{1/n} > 0 $...

Problem: Let $y=x/(1+x)$, where $$\Large x=\omega^{2009^{2009^{\cdots \text{upto 2009 times}}}}$$ and $\omega$ is a complex root of 1. Then $y$ is A)$\omega$ B)$-\omega$ C)$\omega^2$ D)$-\omega^2$ Attempt: I somehow need to show that the huge exponent is of the form $3k$, $3k+1$ or $3k-1$...

Homework Statement In F17, 2 is a primitive 8th root of unity. Evaluate f(x) = 7x3+8x2+3x+5 at the eight powers of 2 in F17. Verify that the method requires at most 16 multiplications in F17. Homework Equations You can can more clearly see the theorem on page 376-378 and the problem is on page...

Homework Statement Expand ##(1+x)^(1/3)## in ascending powers of x as far as the term ##x^3##, simplifying the terms as much as possible. By substituting 0.08 for x in your result, obtain an approximate value of the cube root of 5, giving your answer to four places of decimals. Homework...

Homework Statement Determine the nth roots of unity by aid of the Argand diagram...Homework Equations Is the nth root of unity where we have a complex number to the 'nth' power equal to 1? For example, $$(2+i)^n=1$$ The Attempt at a Solution None yet, still trying to translate the question.

If ##y=x^4##, so x is equal to ##\pm \sqrt[4]{y}## or x is equal to ##\pm \sqrt[2]{\pm \sqrt[2]{y}}## ? Well, I think that x is qual to ##\pm \sqrt[4]{y}## because ## \\y=x^4 \\\sqrt[4]{y} = \sqrt[4]{x^4} = \sqrt[2]{\sqrt[2]{(x^2)^2}} = \sqrt[2]{|x^2|} = \sqrt[2]{|x|^2} = ||x|| = |x| \\ \pm...

Homework Statement A user on math.se wanted to prove that any Mersenne number m = 2^n - 1 has an irrational square root for n > 1. So, it can be proved rather easily that any non-perfect square has an irrational root, and that all of the numbers to be considered are not perfect squares...

$\dfrac {\sqrt {3-3x}+\sqrt {x+6}}{\sqrt {1-4x}+\sqrt {2x+8}}=\dfrac {\sqrt {3-3x}-\sqrt {x+6}}{\sqrt {1-4x}-\sqrt {2x+8}}$ please find :$x$

This may seem like a very elementary question...but here goes anyway. When a positive number is raised to the power 1/2, I have always assumed that this is defined as the PRINCIPAL (positive) square root, e.g. 7^{1/2} = \sqrt{7},. That is, it does not include both the positive and negative...

Hello. I would like to inquire as to how to deal with the said topic title. I'm trying to generate a VLE graph for ethylene oxide-water. While I know that EO will quickly vaporize since the boiling point of EO is quite low, I'm still trying to generate a VLE using SRK. So while the vapor...

Do there exist closed form approximating expressions for the roots of an nth order polynomial?

Find the largest positive real solution to the equation $7x\sqrt{x+1}-3=2x^2+3x$.

Homework Statement Homework Equations See below The Attempt at a Solution Root Locus? Easy Peasy right? Based on provided equation G(s), i solved the coordinates of the root locus diagram using quadratic equation. For the 2nd part of the question, i have to find gain at which rise time...

Homework Statement \int\frac{dx}{\sqrt{e^{x} + 1}} Homework Equations Using u-substitution The Attempt at a Solution Let u = \sqrt{e^{x} + 1} \Rightarrow u^{2} - 1 = e^{x} Then, du = \frac{e^{x} dx}{2\sqrt{e^{x} + 1}} \Rightarrow dx = \frac{2u du}{u^{2}-1} So...

Sorry for any mispellings, English is not my first language. So, I'm studying irrational numbers and I got curious about something and my teacher couldn't give me the answer. I understand Pi must exist because it's the simple result of a division (perimeter by diameter). But how can the...

Homework Statement Solve: \int sin(16x) \sqrt[a]{cos(16x)}\,dx Answer should be linear in the constant "a" The Attempt at a Solution \int sin(16x) \sqrt[a]{cos(16x)}\,dx Set: u=cos(16x), du=-16sin(16x) du ~~\Rightarrow~~ {-1/16}\int \sqrt[a]{u}\,du =...

Homework Statement Points A and B are 10 km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6 km closer to A than B. Show that the location of the explosion is restricted to a particular curve and find...

how do i integrate (x^2 + 2x + 1)sqrt(4x^2 + 8x + 5)??

Homework Statement A:B→B a linear operator Show r is multiple root for minimal polynomial u(x) iff >$$\{0\}\subset \ker(A - rI) \subset \ker(A - rI)^2$$ note: it is proper subsetHomework Equations The Attempt at a Solution Homework Statement My thought: I know ker(A−rI) is basically {{0}...

Homework Statement Let f(z) denote the multivalued function (z^{2} − 1)^{1/2} . Define a branch of f(z) which is analytic in the interior of the unit disk |z| < 1 2. The attempt at a solution Having a bit of trouble getting started. I have rewritten f(z) as ((z-1)(z+1))^{1/2} as...

Homework Statement "At 273 K and 1.00x10^-2 atm, the density of a gas is 1.24x10^-5 g/cm^3. A.) Find the Vrms for the gas molecules B.) Find the molar mass and identify the gas (Choose from H2, He, H20, N2, O2, or CO2)" Homework Equations Vrms = √(3RT/Mm) pV = nRT The Attempt...

Lets say I was trying to figure out the restrictions of a radical equation and the function inside the radical was a cubic function. I know you have to make the equation inside greater than or equal to 0. In the case of a quadratic equation, you have to square root it once you bring everything...

Homework Statement z^3 + (-5+2i)z^2 + (11-5i)z -10+2i =0 has a real root, find all the solutions to this equation. The Attempt at a Solution I have only solved imaginary number polynomials with a given root, but this has no given root, how do I find the real solution? that I can then...

I am trying to prove that √2 is irrational using proof by contradiction. Here is my work so far: √2 = p/q where p & q are in their lowest terms. Where q is non-zero. 2=p2/q2 2q2 = p2 Which tells me that p2 is an even number, using the definition of an even number. We can use this definition...

Homework Statement A tyre contains gas at a pressure of 150 kPa. If the gas has a density of 2.0 kg m-3, find the root mean square speed of the molecules. Homework Equations These are the equations I believe to be relevant: c_{rms} = \frac{\sqrt{<c^2>}}{N} pV = \frac{1}{3}Nm<c^2> p =...

Compute $\sqrt{2000(2007)(2008)(2015)+784}$ without the help of calculator.

Homework Statement ∫(0,1) √x/√[3]1-x Homework Equations \Gammap\Gammaq/\Gammap+q The Attempt at a Solution p-1=1/2 →p=3/2 q-1=-1/3 →q=2/3 β(3/2,2/3)=\Gamma(3/2) \Gamma(2/3)/\Gamma(13/6) \Gamma3/2=1/2\Gamma(1/2)=√π/2 \Gamma2/3=-1/3 \Gamma13/6=7/6 1/6=7/36 β(3/2,2/3)=-6√π/7

Homework Statement The value of √i + √-i , where i=√-1 is (a) 0 (b) 1/√2 (c) √2 (d) -√2 Only one option can be chosen Homework Equations The Attempt at a Solution Let (x + iy)2=i Solving for x and y, I got √i = +1/√2 (1+i) or -1/√2...

Homework Statement Find a power series for f(x) = \frac{1}{\sqrt{4+x^{2}}}, at x=0. 2. The attempt at a solution I have looked up the Taylor series of \frac{1}{\sqrt{4+x^{2}}}, but I don't find any similarity with a power serie like \sum_{n\geq 0} a_{n} x^{n} I don't know how to start...

Homework Statement Hi everyone. I have encountered a weird equation while doing some research and I have no idea how to solve it. The equation goes like this ∫ dR / (1+ c*r) ^ (a/r) = d, limits of integration are from 0 to Rmax, where Rmax ^2 = [u]^2 - α^2, where u is a constant value...

I have started coming across square roots (H+kI)^{\frac 12} of slight modifications of Schrodinger operators H on L^2(\mathbb R^d); that is, operators that look like this: H = -\Delta + V(x), where \Delta is the d-dimensional Laplacian and V corresponds to multiplication by some function. But...

I recently had a friend on facebook share this website Edit by mentor: link deleted it suggests there's a causal relationship between root canals and cancer. Right off the bat, given the website name, realfarmacy, i was skeptical. I tried to check their sources and did a few searches on google...

Homework Statement An ideal gas has rms speed vrms at a temperature of 288K . At what temperature is the rms speed tripled? Homework Equations P=(NmV2)/3V The Attempt at a Solution I'm kind of stumped on this one. Other ones I've done are pretty simple to figure out, but the...

Homework Statement Attached Homework Equations Attached The Attempt at a Solution in my equation for Vrms I am confused to as what values I use for "n" and what "n" stands for in the equation. any help would be greatly appreciated! thanks pf

Hello guys, I need help to sketch the root locus of the system when K is varying from 0 to infinity. (K>=0) The system: http://www.freeimagehosting.net/newuploads/anspe.jpg I'm stuck. I really don't know how proceed. Thanks in advance.

Homework Statement lim x-> 2+ f(x)=sqrt(4-x^2)whats the value of the following function?? Homework Equations The Attempt at a Solution i tried and got the answer as does not exist but some people got it as 0 which is the correct answer

Im just wondering what is the easiest way to deal with calculations where roots are involved? For example how do you solve this one? $$\frac{\frac{1}{2}}{1-\frac{\sqrt{2}}{2}}$$Thank you for replies!

How can I find a primitive root modulo 169? I found the primitive roots mod 13 by testing 2, and then concluding that any 2^k with (k, 12)=1 would do. So that gave me 2, 6, 7 and 11. But modulo 13 I have no idea how to start.. I’m sure there’s a smarter way than trying 2^the orders that divide...

Hello MHB, I got one question. If I want to find basis ker and it got double root in eigenvalue but in that eigenvalue i find one eigenvector(/basis) what kind of decission can I make? Is it that if a eigenvalue got double root Then it Will ALWAYS have Two eigenvector(/basis)? Regards...

Hi everyone, :) Here's a question that I encountered recently. I would appreciate if you could go through my solution and let me know if you see any mistakes or have any comments. Question: Given a linear transformation \(f:\,\mathbb{C}\rightarrow \mathbb{C}\) with matrix...

Which is larger, the real root of x + x2 + ... + x8 = 8 - 10x9, or the real root of x + x2 + ... + x10 = 8 - 10x11?