Root Definition and 918 Threads

Homework Statement Integral: \int\sqrt{1+\frac{1}{a^2+x^2}}\,\text dx Homework Equations The Attempt at a Solution I don't know any method at the moment. Maybe Euler substitution? But this integral is \int\sqrt{\frac{1+a^2+x^2}{a^2+x^2}} after making some calculation, but it...

Hi, Is is correct to say that the logarithm of base 2 of a number x, is the same thing as the square root of a number x?

Hi everybody, I’m trying to compute the square root of the following squared block matrix: \begin{equation} M=\begin{bmatrix} A &B\\ C &D\\ \end{bmatrix} \end{equation} (that is M^(1/2))as function of A,B,C, D which are all square matrices. Can you help me? I sincerely...

The part I don't understand is how they show there exists a smaller element. They assume s=t√3 is the smallest element of S={a=b√3: a,b€Z} . Then what they do is add s√3 to both sides and get s√3-s=s√3-t√3. I don't get how they thought of that or why it works.I know there exists an element...

Homework Statement Finding derivative of (sin(sqt3x+5)) Homework Equations None given. Chain Rule The Attempt at a Solution The answer is: (cos(sqrt3x+5)) * 1/2(sqrt3x+5) * 3 but I don't know how to get to the 3. I turned sin into cos and multiplied by the inside derivative giving the...

Hi all, I want ask you about root programming, if I have the SMM data How I can do the following: 1- Draw the charge, mass and energy distribution of the reaction products 2- Draw the multiplicity of intermediate mass fragments as function of impact parameter and excitation energy...

Here is the question: Here is a link to the question: CALCULUS HELP PLEASE!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hi all, I'm looking for an algorithm for multidimensional constrained root finding, implemented in Fortran. It's intended for finding a steady-state solution for a dynamic model. I have n state variables and n coupled differential equations (n~=60), and I need to find the value for the state...

I haven't taken math in years and am having trouble understanding how to find simplest radical form of a 4√(x14). I said x4√x10. I realize I have 3 x4ths and x2 but I'm not sure if I can pull out more xs. What are the rules for this? Ideas, insight?

Hello everyone! I'm trying to show that $\lim \sup \sqrt[n]{c_{n+1}}=\lim \sup \sqrt[n]{c_n}$ This is my attempt: $\lim \sup \sqrt[n]{c_{n+1}} = \lim \sup \sqrt[m-1]{c_m}=\lim \sup c_m \; ^{\frac{1}{m}}c_m \; ^{\frac{1}{m(m-1)}}$ I'm stuck here, I think I must use some exponential property...

Hi all, I want ask you about root programming , if I have A (mass number) for output and input data for experiment how I can comparison between A input and A output see attachments

Homework Statement Let e be the number close to sqrt(a) by Newtons Method (That is picking a number, diving a by it, and taking their average, divide a by average, get a number, find their average, so on). Using |e<sqrt(a)+e| prove that if |a/e-e|<1/10 then |sqrt(a)-e|<1/10 Note that e is...

Suppose your characteristic equation for the 2nd order equation has complex roots r+ and r- These are conjuagtes of each other so the general solution is: y = Aer+ + Ber- My book chooses the constants A and B as conjugates of each other for the reason that this constructs a real...

Hi, I have a quick question about making quantum mechanics relativistic by simply replacing the hamiltonian by a relativistic hamiltonian. If we write the hamiltonian operator as: H = \sqrt{P2c2 + m2c4}, schrodinger's equation in position basis becomes: i\hbar\dot{\psi} =...

If I have a matrix valued function A(x) of some scalar x, how do I compute the derivative of the square root of A with respect to x? It seems like it should be simple, but I can't find it anywhere on the internet. Thanks!

Is the answer to sqrt -81y^3 : y sqrt-81y? or is there no real solutions? Also for this radical equation: sqrt 2n-5 - sqrt 3n+4=2 I worked it out and can't seem to get an answer. Is there no real solutions?

At first I thought that there is no square matrix whose square is the 0 matrix. But I found a counterexample to this. My counterexample is: \left( \begin{array}{cc} 0 & 0 \\ 0 & 1 \end{array} \right) However it appears that my counterexample has a 0 row. I'm curious, must a square root of...

Homework Statement Ok, working on a inverse function question, and I got stuck with something. Can someone explain the steps that makes this possible here. Something I am missing :( f(x) = √(x^3 + x^2 + x + 1) How is the inverse of the above function this... 3x^2 + 2x + 1 / 2√(x^3 + x^2 +...

Homework Statement p(x)=vx^{n+1}+ux^{n}+1 Homework Equations 1) Find u and v so that 1 is a double root for p. 2) Conclude the quotient of p(x) over (x+1)^2. 3) For n=4 find u and v and find the quotient of p(x) over (x-1)^2. The Attempt at a Solution Can someone just tell me how to...

Homework Statement Sketch the curve of \sqrt[3]{(x^{2} - 1)^{2}}[/b] Homework Equations The Attempt at a Solution I determined that the domain is all real numbers, the x-int. is ±1, the y-int. is 1, the function is symmetric about the y-axis, there are no asymptotes, and here is where I get...

Homework Statement I know how to prove that square root of 2 is irrational using the well ordering principle but what I'm wondering is, how can we use the well ordering principle to prove this when the square root of two isn't even a subset of the natural numbers? Doesn't the well ordering...

I forgot my root password for the Mac OS in which I installed xCode as a separate mountable drive. The only way I can think up right now is to reinstall everything (that is to reset the master password) But I don't want to re-download xCode as it takes a long time to do that. I am new to MacOS...

It can't be x, because you get a positive number when x is negative.

Such as f(x)=(x^2+1)(x+1)?

Homework Statement $$\int \frac{x-1}{(x+1)(x^2+1)} dx$$ Homework Equations N/A The Attempt at a Solution I thought that I would use partial fractions, so: $$\frac{x-1}{(x+1)(x^2+1)} = \frac{A}{x+1} + \frac{B}{x^2+1}$$ $$x-1 = A(x^2+1) + B(x+1)$$ ##x=-1 \Rightarrow (-1)-1 = A((-1)^2+1) +...

Homework Statement Show that x^5 +10x +c=0 has at most one real root on the interval [-1, 1]Homework Equations The Attempt at a Solution I first try to find an x value inorder to find c so i take the end points of the interval and solve for for c -1 +6=-c -5=c 1-6=-c -5=cI get two c's which...

If you could see the image attached, I think it looks better than me typing it here. Didn't know how to embed the image. I would just like to know how it becomes 2v to √2v. EDIT: Ignore. Figured it out. Don't know why I was even baffled. :/

Provided is a function f(x)=\sum_{j=1}^n ||x-x_j||, for x being a two dimensional vector, where ||.|| denotes the Euclidean distance in 2D space. How could one obtain a derivative of such a function?

Hi. I just wondered why we use a 1/\sqrt{V} in the Fourier expansion of the vector potential. A regular 3 dimensional Fourier expansion is just f(\vec r) = \sum_{\vec k} c_\vec{k} e^{i \vec k \cdot \vec r} but as the solution to the equation (\frac{\partial ^2}{\partial t^2} -...

I have to find the limit as x→∞ of √(x2+x)-xI can't rearrange this into a form where I can put infinity into the expression and get a meaningful answer. I've tried taking out square roots to get √x( √(x+1)-√x ) but if I put infinity into this I just get ∞(∞-∞) which is meaningless. Now I know...

Spec of root 2 is that set of elements floor(k * (root 2)) ; k >= 0 . I have no idea of how I can prove the statement in the question. Prove that spec of root 2 contains infinitely many powers of 2. I need ideas on how to proceed. Thank you

When sketching a root locus of a simple closed loop negative feedback system (with positive gain K)... if you have more poles than zeros, we know that they will tend towards infinity along some asymptotes. How do you know which pole will travel along which asymptote? For example in the...

The problem is 28/68=b^14 and I need to solve for b. I get .41176^14 which is not the right answer(which is .93859) What am I doing wrong?

Homework Statement ∫(e^x)/(√4-e^(2x)) Homework Equations arcsin of x The Attempt at a Solution I know how the problem should be solved and have an idea of what the final answer will be. My only question is, how would I take out the four from the square root, in order to make it...

Homework Statement Find dy/dx when y=\sqrt{ln x} Homework Equations d/dx of ln x is equal to 1/x times d/dx of x. The Attempt at a Solution I tried to raise the ln x to the 1/2 power instead of keeping it under a square root sign, but I had no luck. I'm struggling with Calculus. I...

[C++] coding a quadratic root finder with "if statements" //This program solves the qudratic equation #include <iostream> #include<cmath> #include<iomanip> using namespace std; int main() { //Declaring Varibles double coefA; double coefB; double coefC; double x1; double x2; double x3...

Homework Statement 2sqrt (x^2-2), sqrt (4(x^2-2)), x^2. The first 2 formulas are the same thing. However I want to how I would explain the transformation of x^2 to either or of those. I have tried a myriad of things to try get x^2 to any of those other two graphs. A quick answer would be...

Its been a while since I have taken any kind of math class, I am a bit rusty in general algebra. Can someone explain how I would multiply an equation like this (2x-1)sqrtof x-3x is it just like normal distribution? Would I just put the answer underneath the square root? sqrt2x^2-6x^2-x+3x?

Homework Statement I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically. Homework EquationsThe Attempt at a Solution I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I don't get how to find its domain and range...

Hi. I'm currently reading about (negative frequency) solutions to the Dirac equations which can be written on the form \Psi = ( \sqrt{p \cdot \sigma} \chi, \sqrt{p \cdot \bar{\sigma}} \chi)^T e^{-i p \cdot x}For any two component spinor Chi. But the dot product with the four vector p and the...

Finding Limit As "X" Approaches Infinite Of Square Root Function Homework Statement Homework Equations None that I am aware of. The Attempt at a Solution What I tried to do to solve this problem was first, multiplying the function by its conjugate, and then simplifying the...

Homework Statement The image has the question I don't quite understand! Homework Equations The Attempt at a Solution I understand how to get √(√2 - x) but I don't get how they end up with: 4√2 - x ?

On a math test, one of the questions was to solve -\sqrt{7-x}=-\frac{x^2}{2}+12x-10. I solved graphically with a calculator, but later tried to solve algebraically, when I had more time. The equation is equivalent (with extraneous solutions) to x^4 + 48x^3 +536x^2 -956x + 372=0. This quartic has...

Me and a friend was contemplating the ratio of even to odd number in Pascals triangle. After some thought we arrived at a ratio like this when looking at a triangle of 2k-1 rows. \frac{2^{2k-3}+2^{k-2}}{3^{k-1}} - 1 As expected, this ratio grows exponentially. (I.e. almost all numbers in...

Hoping someone can push me in the right direction with this one. Plume snookered. It's to simplify: 2√3(3+√3) Guessing first calculate (a^2 - b^2*c) in the square, though the 2 is throwing this an I'm not sure how the answer is 6√3 + 6, an not 18√3 ?

Homework Statement Here is a picture of the question: Homework Equations The Attempt at a Solution Here it what I did... factored it...so 1 / (x-3)(x+17) domain: (-infinity, -3)(-3,17)(17, +infinity) or rather (-3,17) I know that is not correct. I am really stuck on this one!

Homework Statement \int\frac{1}{x\sqrt[3]{x+1}}dx (That's a cubic root in the denominator, by the way. Not an x cubed.) The Attempt at a Solution I thought possibly partial fractions, but I've never seen it done with a root in the denominator. Integration by parts was...

Could someone please explain how to calculate the nth root of a vector, where n is not an integer?

Homework Statement Prove Square Root of 15 is Irrational The Attempt at a Solution Here's what I have. I believe it's valid, but I want confirmation. As usual, for contradiction, assume 15.5=p/q, where p,q are coprime integers and q is non-zero. Thus, 15q2 = 5*3*q2 = p2...

Homework Statement Prove that there is no rational x such that x2=3 2. The attempt at a solution Suppose that there is a rational x=\frac{a}{b}=\sqrt{3} and that the fraction is fully simplified. (ie. a and b have no common factor) Then a2/b2=3 which means a2=b2.3 and it follows...