Root Definition and 918 Threads

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...

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...

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...

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...

I'm on mobile so I can't use latex. Differentiate: g(x)=√(4-x^4) , x is a set of [-√2, √2] and determine the domains. So I got the derivative which is, g'(x)=(-4x^3) ^1/2 What should I do with the -+√2 ? I don't know what to do next

Homework Statement Derive y= \sqrt(2x^4) - \frac{5}{3x^2} The Attempt at a Solution I am still at the first part of the function (the root): First I tried to derive inside the root like this: \sqrt(2x^4) = \sqrt(8x^3) = 2 \sqrt(2) \times \sqrt(x^3) = \sqrt(2) \times x^2...

Homework Statement Find the 5th root of 36 accurate to four decimal places Homework Equations xn+1 = xn - f(xn)/f'(xn) The Attempt at a Solution First I attempted to write the fifth root of 36 in exponential form as show below: Let the 5th root of 36 = x Let f(x) =...

Does this have to do with the eigenvalues?

What is the fastest algorithm to find the closest root (such that the function value at that point is positive to an error but never negative, if not exactly zero) for a strictly decreasing function?

1. Construct a function f (x) so that Newton's method gets 'hanging' in an infinite cycle xn = (-1)n x0 , no matter how the start value x0 is chosen. 2. Homework Equations : xn+1 = xn - f(xn) / f'(xn) The Attempt at a Solution xn+1 = xn - f(xn) / f'(xn) = (-1)n+1x0 = (-1)nx0 -...

Determine the exact value of... (Square Root of Square Root) I was looking through my textbook and saw a interesting question, I attempted but couldn't get it. (The Answer in Back of Text Book Was Different From Mine..) Question Determine the exact value of... √10+√10+√10... I...

How does one calculate the square root of a quantity of x e.g. \sqrt{25x}? Also could you equate 5x^{2} to 25x? Just a thew random queries going around my head. NOTE: I'm 14.

I know that it isn't. I just want to know how I could, step by step, prove that this function is not differentiable at x=0.

Why the principal nth root is unique ? I mean in the definition of the princibal nth root it says: let x be a real number and n is natural number n \geq 1.if n is odd , the principal nth root of x denoted \sqrt[n]{x},is the unique real number satisfying (\sqrt[n]{x})^{n} = x.if n is even , the...

" Solving this for κ, substituting into (1), and rearranging for G, the result is: " I am trying to rearrange the first equation to make κ the subject and I get: http://www.adamrapley.com/eqn1/CodeCogsEqn%20(6).gif http://www.adamrapley.com/eqn1/CodeCogsEqn%20(5).gif...

Homework Statement \int_{1}^{3}\sqrt{y^2+\frac{1}{2}+\frac{1}{16y^4}}dy Homework Equations The Attempt at a Solution I don't know what to do with this integral, but i do feel like this can be simplified into something much simpler. I tried rewriting it as...

Homework Statement What is the square root of z=-9Homework Equations The Attempt at a Solution Is it possible of me to not use De'Moivre's theorem to solve this question?? Solution : z= \sqrt{-9} z=\sqrt{9} x \sqrt{}-1 z=\pm3 i Will this method be acceptable?? Is this still under the topic...

Homework Statement \sqrt{\sum}x^{2}_{i}\leq\sum|x_{i}|\leq\sqrt{n}\sqrt{\sum}x^{2}_{i} *The sums are all from i=1 to n.* Homework Equations The Attempt at a Solution I'm very new to proof-based math, and just looking for some help to get started with this one. Thanks in advance.

square root in suqare root in square root in square root in... Homework Statement Find the value of: \sqrt{1001\sqrt{1002\sqrt{1003\sqrt{1004...}}}} Homework Equations exponential and surd The Attempt at a Solution I tried to square it but didn't find any patterns because the...

y = \sqrt{x^2- 2x + 1} The y' is always the slope right? Then if we simplify the equation y =\sqrt{(x-1)^2 }----or---y = \sqrt{(1-x)^2} y = x - 1 y = 1-x Checking:---------------Checking: \sqrt{(x-1)^2}-------------\sqrt{(1-x)^2}...

Hi! I have to solve a system of two coupled nonlinear ordinary differential equations. In the function that defines the system there are terms with square root of the dependant variables. I tried to solve the system numerically but in the nmerical solution I get violent oscillations. Then I...