Root Definition and 944 Threads

\lim_{x\to +\infty}\sqrt{x^2+3}-x sorry first of all how do you turn this string into latex I don't see the icon tool on the editor thnx

How do you prove that there does not exist numbers a,b\in\mathbb{Q} such that 0 = a + b\sqrt[3]{2} + \sqrt[3]{2}^2

Homework Statement Show that there exists one root int (0,2) of the following function: f(x)=(1-x^2)^2-√((1-x^2)*(1-1/2*x^2)) Homework Equations The Attempt at a Solution I first found: f(0)=0 and f(2)=7.268 But, i don't know what to do now. I'm not sure if it has...

I have a 4th order differential equation with given -2 +3i root. Now need to find the homogenous solution. Well, if the root was real, it would be easier but now I'm stuck and don't know how to proceed. What am I supposed to do to solve this ? Equation is : d4y(t)/dt4 +6d3y(t)/dt3 +...

when installing ROOT in ubuntu 11.10 i have the following message name@ubuntu:~/root$ ./configure Checking for source directory ... /home/waleed/root Configuring for linuxx8664gcc Checking for GNU Make version >= 3.80 ... ok Checking for C compiler ... gcc Checking for C++ compiler ...

Hi Let \( c>0 \) be a real number. Then I am trying to prove that \( \forall\; n\in\mathbb{N}\; (c^{1/n} >0) \). I let \(n\) be arbitrary and then tried to use method of contradiction. But ran into difficulties. Is there another approach ?

Homework Statement Let a be a positive real number. Prove that if a is irrational, then √a is irrational. Is the converse true? Homework Equations So, an irrational number is one in which m=q/p does not exist. I understand that part, but then trying to show that the square root of an...

Homework Statement Let nεZ>0. Prove that: Ʃ1/√(i) ≥ √(n) The Attempt at a Solution I'm not sure where to begin, this feels like it should be an induction problem, but I'm not sure how to show that √(n) + 1/√(i+1) ≥ √(n+1). There doesn't seem to be any obvious algebra that would...

Root Mean Square Uncertainty [solved] My TA gave us a paper after this assignment regarding how to do Root Mean Square Uncertainty, however I can't read her handwriting... I think I get the gist of it, but It's written so strange I need to check. Is it sqrt(...

Homework Statement Prove that Prove that the equation has at least one positive real root, using the Intermediate Value Theorem on an appropriate function. 3 arctan(2x-1)=cos^2(x-(∏/6)) + 1 Homework Equations No clueThe Attempt at a Solution I honestly speaking have no clue how to even...

Hi. I am currently doing an experiment regarding to the factors affecting beet root cell membrane. Some of them are pH (2,4,6,8,10) , Ethanol (1%, 25%, 50%) and Detergent(1%, 5%). I've seen that different pH, different concentration in ethanol and detergent each has different results in both...

Homework Statement Solve \sqrt{-e^{(i2\pi)/3}} Homework Equations The Attempt at a Solution I seem to be missing something simple, as I take: \sqrt{-1} = i then, e^{(1/2)*(i2\pi)/3} which comes out as: ie^{i\pi/3} however, the solution is: -ie^{i\pi/3}, and I can't seem to see where...

Homework Statement Given that 2 is a repeated root of the equation 2x^3 + px^2 + qx -4 = 0, find the third root and the values of p and q. Homework Equations b^2 - 4ac(?) The Attempt at a Solution Since it said 2 is a root I plugged in 2 as the value of x and rearranged the...

i just want to make sure I'm doing this correctly as there is some discrepancy in my textbook. i know the centroid is equal to (Ʃpoles - Ʃzeros) / (# of poles - # of zeros) the equation i have is s2 + 2s + 8 / s(s2 + 2s + 10) so the zeros are -1 + i√7 and -1 - i√7 and the poles are 0, -1...

Homework Statement Do not use a calculator for this problem. Express your answers using square roots and/or fractional multiples of x. Determine the complex constant c such that v is a root of: z6 - c = 0 Homework Equations v = \sqrt{3} - j The Attempt at a Solution I believe...

dimensionless ODE $\displaystyle\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$ $\displaystyle U=r-\frac{ru}{q}$ and $\displaystyle V=\frac{u}{1+u^2}$ Show using conditions of a double root that the steady state is given parametrically by $\displaystyle...

Homework Statement Show \lim\limits_{n\to\infty}\sqrt[n]{\frac{1}{n^2}}=1 Homework Equations The Attempt at a Solution No ideas

r,q are constants. I need to factor this equation such that there is a double root. -\frac{r}{q}u^3+ru^2-\left(\frac{r}{q}+1\right)u+r=0 Are there any tricks for this because this just a nasty equation. I don't know if that is a wise approach but: (au+b)(cu+d)^2 =...

Dear Forum Users, I have got more math question rather then the physics question. Does someone know if: \mid d(x)\mid^2 equals just d(x), here d(x) is just the Dirac delta ? best regards, nykon

I need to factor x5 - 1.I know (x-1) is a factor and have gotten: (x-1)(x4+x3+x2+x +1) I'm not sure where to go from here. Thanks in Advance.

Hello Friends, I have a question of calculating a cube root of large number like 24 digit number. I calculated by means of Wolfram but I want to try it myself on paper. Is there a method such as Calculus or Algebraic to find the cube root? Thank you. P.S. I want to use the method for...

Homework Statement Simplify \sqrt {10 + \sqrt{24} + \sqrt{40}+\sqrt{60}} Homework Equations \sqrt{a+b+2\sqrt{ab}} = \sqrt{a}+\sqrt{b} The Attempt at a Solution \sqrt {10 + \sqrt{24} + \sqrt{40}+\sqrt{60}} = \sqrt {10 + 2 \sqrt{6} + 2 \sqrt{10}+ 2 \sqrt{15}} Stuck...

Homework Statement Prove that z=e^{\frac{2k\pi i}{n}},n\in\mathbb{N},k\in\mathbb{Z}, 0\leq k\leq n-1 is an n-th root of unity. The Attempt at a Solution So I know I have to come to the conclusion that z^{n}=1. I'm thinking of using the property e^{i\theta}=cos\theta+isin\theta, but...

Homework Statement z = (n + i)^{2} n is a positive real number, and arg(z) = \frac{\pi}{3} Find the value of n. The attempt at a solution I am reviewing old problem sets from years past, and came across this problem that appears pretty simple. I have my old answer as n=\sqrt{3}...

Homework Statement scientific notation I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power Homework Equations 4 . .... ... ... -9 ... sq rt of 5.2 X 10 4 -9 sq rt of 5.2 X 10 The Attempt at a Solution The answer I...

why there is no answer when negative value is being square root? e.g: square root of -9 when i try to find answer from calculator, ''math error '' appears.. so is there an explanation for this question?? this question may looks so weird..but i m juz asking out of curiousity..

Can a kind person explain to me why I appear to have two conflicting solutions to: \int^{\frac{1}{\sqrt{2}}}_0dx\sqrt{1-x^2} Solution 1 : Standard trigonometric substitution: x=\sin\theta Integral becomes...

Homework Statement Prove: If \lim_{x \rightarrow a} f \left( x \right) = l , then, if \sqrt[n]{f \left( x \right)} exists, \lim_{x \rightarrow a} \sqrt[n]{f \left( x \right)} = \sqrt[n]{l} . Homework Equations Nothing really... The Attempt at a Solution Okay, so here goes...

I need some help with understanding the basics of Lie algebra theory. I suspect my problems are due to a fundamental misunderstanding somewhere so apologies in advance for the naivety of the questions and for the restatement of elementary mathematics. As I understand it elements of Lie groups...

The problem asked to prove by contradiction that the function has only one real root. They used Roll'es theorem and proved that f ' (x) =/= 0 then they concluded that because f ' (x) =/= 0 then by contradiction the function can have atleast one real root... Look at the picture it has the...

Please see attached. This is a general question for a more complex thermo problem, but it fits this form. Are there any tricks to getting expressions out of square roots in solving DEs? y=y(x) x=x(t) I want to get y by itself so I can integrate with respect to x, but it is trapped in a...

How in the world do you take the square root of a matrix in Mathematica? All the ways I've tried haven't worked... Thanks!

What is the root source of "Light"? I'm not talking about converted/transformed energy via external sources, i.e. Electricity or heat transformed to Light. Whats the root source? Energy itself?

Homework Statement What I am confused about is: x - \sqrt{2}=0 x=\sqrt{2} is it equal to x=\pm\sqrt{2} ? Homework Equations The Attempt at a Solution The way I know it, those two are not equal. But my teacher insists on saying that whenever there is a square root, we should always...

Homework Statement I am trying to prove that f(x)=x^{4}-x-1 has exactly one root on [1,2]. Homework Equations The Attempt at a Solution Step one, by intermediate value theorem I proved that there is at least one root on [1,2]. But I don't know how to go about proving there is...

Homework Statement Let f be a quadratic polynomial function of z with two different roots z_1 and z_2. Given that a branch z of the square root of f exists in a domain D, demonstrate that neither z_1 nor z_2 can belong to D. If f had a double root, would the analogous statement be true?Homework...

Homework Statement Let A be the matrix: -5 -3 18 10 Find an invertible matrix X so that XAX-1 is diagonal. Use this to find a square root of the matrix A. Homework Equations DetA - xI (A-\lambdaI)v = 0 The Attempt at a Solution So, I found DetA- xI, which...

Using ΔX=XH-XL as one of the convergence criteria in regula falsi may lead to infinite looping, e.g. f(x)=0.5x-2ln(x), with a bracket [7,10]. A better choice is to use the approximation error ΔX=|ΔXR|, i.e, the difference between the current estimate and the previous estimate of the root...

Firstly, the set E is defined: "Let E be the set of all positive real numbers t such that tn<x." Later on the proof goes: "Assume yn>x. Put k=yn-x / nyn-1. Then 0 < k <y. If t ≥ y - k, we conclude that yn-tn ≤ yn-(y-k)n < knyn-1 = yn-x. Thus tn>x, and t is not a member of E. It follows...

Homework Statement I need to evaluate this particular integral and I'm confused on what method to use. I'm currently learning integration calculus and I tried doing some introduction on electromagnetic field. Quite unexpectedly the integral turned to be heavy. \int_{-a}^a...

How to find value in root finding exercise? I am designing a fountain for a Vegas hotel which sprays water in the shape of a hyperbola onto a screen. The hyperbolas shape is a function of several different variables. I am looking for conditions which will cause the area cast by the bottom and...

In Ramakrishna's paper, http://arxiv.org/ftp/arxiv/papers/1111/1111.1922.pdf , he derived equation (9), page 5. It is a difference of two square-roots using an approximation method. Can anyone help in how this is done? Thanks

a,b,c are integers not all equal and w is the cube root of unity then minimum value of |a+bw+cw2|(w is not equals one). My answer |a+bw+cw2|<=|a|+|bw|+|cw2| |a|+|bw|+|cw2|=a+b+c. so at lest one value of |a+bw+cw2| will smaller than the minimum value of a+b+c. for integers this minimum...

Homework Statement I'm this series to see if it's convergent or divergent. I tried the root test, but it came out inclusive, and now I am trying to figure out if the ration test works. The only thing I'm asking which would be the right test for this. Homework Equations ∞Ʃn=1...

Homework Statement if m, n are distinct odd primes, show that the set of units mod mn has no primitive root. Homework Equations [ hint: phi(mn) = (m-1)(n-1) so we can show for a, a unit mod mn, a((m-1)(n-1))/2 = 1 ] and a \equiv b mod mn iff a\equiv b mod m and a \equiv b mod nThe Attempt at...

Is there a good way to do this? I have an equation, say x^3 - 4*x^2 + 2, so a=1, b=-4, c=0, d=2. Is there an easy way to express the largest root of such an equation? In this case, the roots are: 3.8661982625090223 -0.65544238154983 0.7892441190408067 But I am trying to find an...

Hello, I do not understand very well how to sketch a root locus plot. I am able to find poles/zeros, where the root locus exist on the real axis, the break away/in points, intersection of asymptotes, crossing of the imaginary axis, etc., but I do not understand how to actually draw the root...

Homework Statement Use the Intermediate Value Theorem and Rolle's Theorem to show that f(x) = 2x-2-cosx has exactly one root. Homework Equations The Attempt at a Solution I'm not really sure what the question is asking for. the theorems I believe are to prove the existence of a...

Homework Statement Does the principal branch square root of z have a Laurent series expansion in the domain C-{0}? The Attempt at a Solution Well I'm not really sure what a principal branch is? I believe that there is a Laurent series expansion for z^(1/2) in C-{0} because originally our...

Homework Statement Hello. I'm trying to solve this equation: 16.9038=\sqrt{1470tan\theta} Homework Equations The Attempt at a Solution I just need to know what theta is. It's been a while since I've calculated something like this and just need someone to show me the steps...