Root Definition and 918 Threads

Homework Statement determine whether the series (1-1/n^(1/3))^n converge or diverge Homework Equations all the testing procedure The Attempt at a Solution So I did the root test first, but the limit on the inside is 1. I then tried the ratio test but then when I tried taking the...

Homework Statement Im trying to prove that if p is prime, then its square root is irrational. The Attempt at a Solution Is a proof by contradiction a good way to do this? All i can think of is suppose p is prime and √p is a/b, p= (a^2)/ (b^2) Is there any property i can...

Hi everyone, :) Here's a question that I don't quite understand. What I don't understand here is what is meant by root space in the context of a linear transformation. Can somebody please explain this to me or direct me to a link where it's explained?

Hi, I am trying to make progress on the following integral I = \int_0^{2\pi} \sqrt{(1+\sum_{n=1}^N \alpha_n e^{-inx})(1+\sum_{n=1}^N \alpha_n^* e^{inx})} \ dx where * denotes complex conjugate and the Fourier coefficients \alpha_n are constant complex coefficients, and unspecified...

Homework Statement Use Newtons method to compute the cube root of 5. Do the first 10 iterations. x_{(0)}=1 determine the fixed points of the iteration and determine whether they are repelling/attracting. if attracting, then determine if the convergence is linear or quadratic. draw the...

\sqrt{\frac{x-3}{x}} = \frac{\sqrt{x-3}}{\sqrt{x}} that is not true for all x, it is true for x\in [3,\infty) I want to teach my students that the exponents distribute over fractions unless we have a case like that square root or any even root. what do you think ?

Homework Statement I am doing a problem of a contour integral where the f(z) is z1/2. I can do most of it, but it asks specifically for the principal root. I have been having troubles finding definitively what the principal root is. Anyplace it appears online it is vague, my book doesn't...

I was looking over this proof and I have some questions: http://jeremykun.com/2011/08/14/the-square-root-of-2-is-irrational-geometric-proof/ Second paragraph, what does "swinging a b-leg to the hypotunese" mean? Also, where did the arc come from, I really don't understand also, the last part...

I found this on the internet, but did not find the proof. Curious to me is that the the ratio and root test have the same conditions. How can i basically prove this equality? $$\frac{a_{n+1}}{a_{n}} = \sqrt[n]{a_{n}}$$ Thank you!

Homework Statement Evaluate derivative of (sin sq. root x) w.r.t x? Homework Equations Limit Δx--> 0 (sin√(x+Δx) - sin(√x)) / Δx The Attempt at a Solution i couldn't operate it from here... Δy = (2cos((√x+Δx) + (√x)) . sin((√x+Δx) - (√x)) / Δx...?

I found that the cartan subalgebra of ##sp(4,\mathbb{R})## is the algebra with diagonal matrices in ##sp(4,\mathbb{R})##. Now to find out the roots I need to compute: ##[H,X]=\alpha(H) X## For every ##H## in the above Cartan sublagebra, for some ##X \in sp(4,\mathbb{R})## Now, I know that...

Given $$f(x)=5tx^4+sx^3+3rx^2+qx+p$$ for $f(x)\in R$. If $r+t=-p$, prove that there is a real root for $f(x)=0$ in $[-1,1]$.

I'm trying to compute following integral (Wolfram doesn't give answer): \int\sqrt{E-Bk^{2}\frac{cos^{2}(kr)}{sin^{2}(kr)}-k\frac{cos(kr)}{sin(kr)}\sqrt{D+Fk^{2}\frac{cos^{2}(kr)}{sin^{2}(kr)}}-\frac{Ak^{2}}{sin^{2}(kr)}}dr where A,B,C,D,E,F,k are constants. Substitution t=sin(kr) leads to...

Here's my problems: How might you "rationalize the denominator" if the expression is \frac{1}{2+7√2+5√3} or \frac{1}{\sqrt[3]{2}+1}? I know that in typical problems where we rationalize the denominator, we simply have to multiply the denominator and numerator by the conjugate of the denominator...

Find the real root of $$x^5+5x^3+5x-1$$

Hi, I know how to rationalize a denominator when it is a square root monomial or a square root binomial (through conjugation). For example, for a square-root monomial: 5/√25 = [5(√25)]/ [(√25)(√25)] = [5(√25)]/25 = (√25)/5 = 1 or -1and, for a square-root binomial: 5/(5 + √25) = 5(5 -...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

How would you integrate it? \int \frac{d \varphi}{\sqrt{1 + \frac{a^2 b^2 \sin^2 \alpha}{(a \sin \varphi + b \sin (\alpha - \varphi))^2}}} I know that solving it numerically would probably be easier, but I would prefer a closed form solution in this case.

Hello I am working on this integral \[\int \frac{\sqrt[3]{x}}{(\sqrt[3]{x}+1)^{5}}\]I have tried using a substitution, I did: \[u=\sqrt[3]{x}+1\] and I got that the integral becomes: \[3\cdot \int \frac{(u-1)(u-1^{2})}{u^{5}}du\]I moved on from there, got a result, however it was not...

I have a question for a programming exercise I'm working on for C. The problem is to "Write a program that uses Newton's method to approximate the nth root of a number to six decimal places." The problem also said to terminate after 100 trials if it failed to converge. Q1. What does "converge"...

Homework Statement x4 - 4(x3) + 3(x2) -2x +1 = 0 Homework Equations Rational Root Theorem, q/p The Attempt at a Solution Hello everyone. Today, I've learned the rational root theorem( it's a bit late, isn't it? :( ) and thus wanted to see how it works. According to the...

Homework Statement Get the value of a if \sqrt{6-\sqrt{a}}+\sqrt{6+\sqrt{a}}=\sqrt{14} The Attempt at a Solution nothing succesfull Feel free to move this thread,..I actually place it here to tap more brains

Hello, I've been trying to find online where I could calculate my grade based off a college curve. So the average grade on the test was a 63. The RMS is 16. I got a 86. So what will my grade curve to? This is out of 50 people. Also, the professor curves to a 70 (I think).

Homework Statement Let f:R→R be a continuous and differentiable function, then prove that the equation f'(x)+λf(x)=0 has at least one real root between any pair of roots of f(x)=0, λ being a real number Homework Equations The Attempt at a Solution All that I know from Rolle's Theorem is...

Homework Statement show that the equation x^3-15x+C=0 has at most one root on the interval [-2,2] Homework Equations The Attempt at a Solution I know I need to use Rolle's theorem but I'm not sure how to find the answer. Thanks.

I'm comparing the shear formula for a beam in english and metric. But it seems the formula or result don't match. In English, the formula is Vc=2*b*d*sqrt(Fc) Given b=11.81102 inches d=18.11024 inches fc=4000 psi Vc=2*b*d*sqrt(Fc)=27056 lbs Now converting the units in metric...

How many integers satisfy [SIZE="2"]{√n-√(23×24)}^2<1 I was able to solved this by trial and error method , but i want to know systematic step-wise solution.

I wonder how do I find the root of 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, and so on? And why the circle and the curve looks so smooth in the computer graphic software such as AutoCAD, Adobe Illustrator, etc., if the root is can not be found? It should be looks rough. Thank you

Hi, Consider the algebraic function w(z) given by the expression f(z,w)=a_0(z)+a_1(z)w+a_2(z)w^2+\cdots+a_n(z)w^n=0 where f(z,w)is irreducible over the rationals, and the coefficients, a_i(z), polynomials with rational coefficients . Let z_s be a point such that f(z_s,w)=0 has roots with...

Hello MHB, I got stuck on integrate this function $$\int \frac{\sin^3(\sqrt{x})}{\sqrt{x}}dx$$ my first thinking was rewrite it as $$\int \frac{\sin^2(\sqrt{x})\sin(\sqrt{x})}{\sqrt{x}}dx$$ then use the identity $$\cos^2(x)+\sin^2(x)=1 \ \therefore \sin^2x=1- \cos^2(x)$$ $$\int...

Homework Statement Derive cube root formula using Newton-Rhapson's method. x - y^3 = 0. Homework Equations xn + 1 = xn - f(xn)/f'(xn) The Attempt at a Solution I know that the solution is (2y + (x/y^2))/3 I tried using implicit differentiation and stuff but I can't get this out...

Show that if $x$ is a primitive root of p, and $x^{p-1}$ is not congruent to 1 mod$p^2$, then x is a primitive root of $p^2$

Hi everyone I have these 2 integrate that I can't solve, I have tried them with mathematica and wolfram, but they can't find an answer, maybe someone have an idea on how I could tackle these 2 bad boy! The first one is $$\int{ \sqrt{ \frac{1+( \frac{1}{10}+ \frac{s}{25})^2}{ \frac {s}{10}+...

If at 120 K the Vrms is v , then at 480 K it will be a. 1 b. 2 c. 3 d. 4 Which formula is to be used here? Plz solve this.

Homework Statement 4. Implement a simple method to find the square root of a double precision floating point number x. A simple method is to consider the error produced by a “guess” y of the solution. Square the value y and compare with the value x. If y is correct, the error e=|y2-x| where ||...

$\sqrt {x}+\sqrt {y}=35$ $\sqrt [3]{x}+\sqrt[3] {y}=13$ find x+y

I feel kind of ridiculous making this post, but here we go: What would be the correct answer to this question; Choose all the number sets (natural, integer, rational, or irrational were the only options given) that -√81 belongs to, and show how you found your answer. What I said was this...

[FONT=CMR12]let p be an odd prime. Show that if there is a primitive root of p^n, then there is a primitive root of 2p^n. Strategy? [FONT=CMR12]

1. Find the intervals of increase and decrease 2. C(x)=x^{1/3}(x+4) 3. C(x)=x^{4/3}+4x^{1/3}; C'(x)=\frac{4}{3}x^{1/3}+\frac{4}{3}x^{-2/3}=\frac{4x^{1/3}}{3}+\frac{4}{3x^{2/3}}=\frac{x^{2/3}}{x^{2/3}}*\frac{4x^{1/3}}{3}+\frac{4}{3x^{2/3}}=\frac{4x+4}{3x^{2/3}} I am wondering...

Homework Statement Can you if given a sigma notation for an infinite series Ʃ 2^n/(4^n+1) rewrite as, Ʃ 2^n/(4^n+1^n) then doing the root test can you lim n→∞ n^√abs((2/(4+1))^n) which equals 2/5, and 2/5<1, therefore can i conclude that the series above converges? Sorry...

Is there any method to find the exact value of the square root of 3,5,7,11,13,14,15,17,18, etc.? Thank you

Hello PF members, I want to solve this integral but I cannot find a method. \int\sqrt{1 - 2sin(x)}dx for 0 < x < ∏/6 Or more generally \int\sqrt{a - bsin(x)}dx for a > b How can I solve this? Thanks in advance

Homework Statement Solve each inequality without graphing the corresponding function. State the solution algebraically and graph on a number line: x/x2-9≤0 so i factor out the denominator and get (x+3)(x-3) the root here is zero, but for some reason in the chart (for rational/reciprocal...

Hello everyone.. Homework Statement ∫√((1+(e^-x))^2)dx 2. The attempt at a solution I first tried to do a u sub and then attempt a trig sub however I can't do anything with the e^-x left in the u sub. Does anyone have another way I can integrate this thing?? Thank you for any suggestions/help!

Homework Statement Let G be a finite group in which every element has a square root. That is, for each x in G, there exists a y in G such that y^2=x. Prove every element in G has a unique square root. Homework Equations G being a group means it is a set with operation * satisfying...

Homework Statement |x3sqrt(4-x2)dx Homework Equations uv - | vdu The Attempt at a Solution u = x2 v = -1/3(4-x2)3/2 du = -2xdx dv = x(4-x2)1/2 uv - | vdu x2(1/3)(4-x2)3/2 - | 1/3(4-x2)3/2(2xdx) x2(1/3)(4-x2)3/2 +(1/3)|(4-x2)3/2(2xdx) u = 4 - x2 du = -2xdx...

I am reading about the root mean square and Parseval's Theorem but I don't understand how we find $A_0$. So it says the average $\langle x\rangle$ is zero and the $x_{\text{RMS}} = \sqrt{\langle x^2\rangle}$ where $$ \langle x^2\rangle = \frac{1}{\tau}\int_{-\tau/2}^{\tau/2}x^2dt $$ The Fourier...

Homework Statement I'm trying to see if I can prove that any non-square number's square root is irrational. I'm using only what I already know how to do ( I like trying to prove things myself before looking up the best proof), so it's going to be round-about. Attempt#1 Eventually required me...

[FONT=arial]A function f has a root of multiplicity $m>1$ at the point $ x_*$ if $f(x_*)=f'(x_*)=...=f^{(m-1)}(x_*)=0$. Assume that the iteration$ x_{k+1}=x_k-mf(x_k)/f'(x_k)$ converges to $x_*$. If$ f^{(m)}(x_*)≠0$, prove that this sequence converges quadratically.(We may use the Taylor's...

I don't understand what I have to do with this question. do i just explain what is happening in each part or is there more to it? http://imageshack.us/scaled/medium/826/screenshot20130214at150.png Thanks