Root Definition and 918 Threads

I can't figure out Derivative of (sq. rt of x)^x Can anyone help me?

Homework Statement integrate sqrt(1-x^-2/3)^1/2. Homework Equations The Attempt at a Solution The only thing I can think of is u substitution with u = 1 - x^-2/3. Obviously this cannot work because du differs by more than just a constant. I guess I need to somehow factor...

I want a MATLAB code to draw the root locus for a characteristic equation of a transfer function of unity feedback, also what is the range of K that keeps the system stable , here is the characteristic equation: s^5+600s^4+50000s^3+ks^2+24ks+80k=0 please help, thanks in previous

Hi everyone :smile: When determining the radius of convergence of a power series, when should I use the ratio (a[sub n+1] / a[sub n]) test versus the root (|a[sub n]|^(1/n)) test? I know that I'm supposed to use the ratio only when there are factorials, but other than that, are these tests...

Hi, Apologies for the trivialness of the question, but I'm not so great at this. I was wondering why the square root of a real number is positive. Why is sqrt(9) = 3, and not -3 as well, since (-3)² would give 9. Is it just a condition you set, that the function values must be positive? At...

Happy Square Root Day all. Today, 3/3/2009, is square root day because 3 \times 3 = 2009. That's as good a reason to have friends over for a beer as any. http://www.myfoxdc.com/dpp/news/dpg_Math_Fans_To_Celebrate_Square_Root_Day2223492"

I NEED TO GET A DERIVATION SO THAT I CAN MATHEMATICALLY UNDERSTAND WHY: The peak voltage or current is divided by square root 2 to get the root mean square value.please i need a simple derivation just to understand,i will be very greatful for ur consideration.thankyou.

\int \frac{dx}{x(1+2\sqrt{x}+\sqrt[3]{x})}=\int \frac{dx}{x(\sqrt{x}+1+\sqrt{x}+\sqrt[3]{x})}= \int \frac{dx}{x(\sqrt{x}+\frac{(1-x)}{1-\sqrt[3]{x}})} i got read of one root but instead i got another one ??

i tried this: \int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}=\int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}*\frac{1+\sqrt{x+1}}{1+\sqrt{x+1}}*\frac{1-\sqrt[3]{x+1}+(x+1)^{\frac{3}{2}}}{1-\sqrt[3]{x+1}+(x+1)^{\frac{3}{2}}} but when i got read of 2 roots i got another two roots which are more...

Homework Statement If w is a complex cube root of 1, prove that x + wy + w^2z is a factor of x^3+ y^3 + z^3 - 3xyz, and hence factorise the equation completely. Homework Equations Complex cube root of 1 = -1/2 +/- 3^1/2/2 i The Attempt at a Solution Erm, I feel way over my head...

Homework Statement the value of f(x) = (sqrrt e^x +3) at x=0.08 obtained from the tangent to the graph at x=0 is...? Homework Equations The Attempt at a Solution i used linear approximation. (sqrrt e^o +3) + (1/2(sqrrt3+e^0)(0.08) i got an answer but i know its wrong. i...

Given that the root mean square (RMS) of a sine function is as follows: RMS of (a*sin(\omega*r) = a / \sqrt{}2 Let a = 1/\omega Thus RMS of ((1/\omega)*sin(\omega*r)) = 1 / (\omega*\sqrt{}2) But for sinc(\omega*x), what is formula for the RMS?

i am given this function and need to integrate it \frac{4x+7}{\sqrt{-4x^2+20x-9}} i have been trying to intergrate it by calling something T, preferably the expression under the sqrd root, or part thereof (-4x2+20x=T) but i can't find the way to do this, can't find the best expression that...

Hi, I'm having trouble understanding some statements in this proof from my textbook: "Thus, 2 = s^2/t^2 and 2t^2 = s^2. Since s^2 and t^2 are squares, s^2 contains an even number of 2's as prime factors (This is our Q statement), and t^2 contains an even number of 2's. But then t^2 contains an...

I want to find the value of r such that: sqrt[(r^2)+(110^2)] + r = 160 Is there a way of doing it? I have found a solution through trial and error (1dp). But I want a method of finding an exact answer. Thanks

I have to find the "second smallest root" of the following equation : 1-x+(x^2)/(2!)^2-(x^3)/(3!)^2+(x^4)/(4!)^2+...=0 Matlab returns quite a satisfactory answer. >> p=[1/518400 -1/14400 1/1576 -1/36 1/4 -1 1] p = 0.0000 -0.0001 0.0006 -0.0278 0.2500 -1.0000 1.0000...

Homework Statement What is the deriv. of the square root of (xy)? Homework Equations The Attempt at a Solution I used the chain rule: (1/2)(xy)^(-1/2) times (y + x(dy/dx)) i am unsure on how to distribute this correctly

Homework Statement let the complex number 1 = 1 + 0i. Show this number has three cube roots. Use any means to find them. Homework Equations not sure. cubic root x means there is some number y, x = y*y*y. The Attempt at a Solution Well one root has to be 1 Another is...

Is there an easy (by which I mean an algorithm polynomial in size of input) way to know whether in the multiplicative group of integers mod P (P is a prime), whether an element is a generator or not?

Homework Statement An AC generator produces a voltage of peak value V. The frequency of rotation of the coil of the generator is doubled. The r.m.s. value of the voltage produced is Homework Equations The answer is V multiplied by \sqrt{}2 but I don't understand why. The Attempt at...

Homework Statement prove that if n is a natural number greater than 0, then sqrt(n^2 + 1) is not a natural number. Homework Equations The Attempt at a Solution I can't tell if I am right, which probably means that I am not. Assume sqrt(n^2+1) is a natural number. Then there is...

Square Root Of 2 (from Hardy "Course Of Pure Mathematics") I was surprised to find it in my local bookstore amidst math "cheat" books in the one-shelf math section (and the fact that it was the last copy left... ??). Is he asking to simply carry out the calculation? Or is he asking to...

Hi all :D, Is there such a thing as fundamental equations that are at the root of all physics? Thanks PS If yes- then please provide a link to it if possible. Thanks

Hi, I have a non-linear function F: \Re^{3}\rightarrow\Re. I would like to find the roots of this equation numerically, since an explicit formula cannot be derived. As far as I am aware Newton's method can only be utilized when the domain and the range of the function are of the same...

i wrote the question and how i tried to solve it this link http://img514.imageshack.us/img514/5053/img9151yd0.gif

Hi, I was taking a square root of a fraction and I was wondering how to get a fraction result after I've taken the square root of it. And it also made it think; How do I take a root of a number in pen and paper, without the use of calulators? Can anyone help me? Thanks

Hi all, I've been musing on a problem I came across whilst decanting some sloe gin (that time of the year here in the UK and all that). Essentially, I want to know given a vessel of known dimensions, open to the atmosphere at the top, with a hole in the bottom, and a pipe at the top filling...

y = 2x square root of (x^2+1) I'm not exactly sure how to start off this problem. Am I supposed to use the chain rule or some other rule? I really need help on understanding this, so if anyone is kind enough to provide detailed steps, I thank you so much.

show x^3-15x+c=0 has at most one root on the interval [-2, 2]. My work/attempted solution. Using the IVT i determined that there is a possible root (N=c) within the interval of [-2,2]. because c is my constant i decided to Use [d] as my letter for explanation. f(x)=x^3-15x+c...

prove that the square root of 2 plus the square root of 3 is not rational? does always the sum of two not rational numbers is a not rational number? i know the proof 2 = a^2/b^2 i separately proved that square root of 2 and square root of 3 are irrational how two prove that the sum...

Homework Statement Find an interval of length 1 that contains a root of the equation xe^{x}=1 Homework Equations The Attempt at a Solution I'm not quite sure how to find these intervals... Homework Statement Find an interval of length 1 that contains a root of the equation...

Homework Statement Suppose T \in L(\textbf{C}^3) defined by T(z_{1}, z_{2}, z_{3}) = (z_{2}, z_{3}, 0). Prove that T has no square root. More precisely, prove that there does not exist S \in L(\textbf{C}^3) such that S^{2} = T. Homework EquationsThe Attempt at a Solution I showed in a...

How do you show that the cubic root of two + the square root of two is irrational? I can easily show that each of these numbers is irrational, but not the sum :/.

Homework Statement Show that the equation 2x-1-sin(x) = 0 has exactly one real root. Homework Equations The Attempt at a Solution I first used the Intermediate Value Theorem to prove that there exists at least one c such that f '(c)=0. The next step requires Rolle's Theorem to...

Homework Statement to six decimal places the root of the equation e^-x=lnx over interval [1,2] The Attempt at a Solution (e^-x)-lnx=0 F'(x) = (-e^-x)-(1/x) x(subcript(n))-(e^-x)-lnx/(-e^-x)-(1/x) the problem I am having is getting it to six decimal places. do i have to go int0...

Homework Statement I'm trying to analyze the root locus of this transfer function in Matlab to control a DC motor: mysys=tf([0.022],[0.00000000007 0.0000000626 0.000493]) The Attempt at a Solution Using: %[Kp,P]=rlocfind(mysys) %rltool(mysys) rlocus(mysys) I get a root locus...

Homework Statement Let G be a finite group in which every element has a square root. That is, for each x\epsilon G, there exists y \epsilon G such that \(y^2=x.\)Prove that every element in G has a unique square root. The Attempt at a Solution Proof: Assume not. Let k be the order of G...

Homework Statement Suppose that f(x) is a polynomial of degree n with real coefficients; that is, f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real) Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x) Homework Equations...

I know this must be an easy question, but I can't seem to remember how to do it: \sqrt{z^2+R^2 - 2zR} - \sqrt{z^2+R^2 + 2zR} Can someone go through step by step how to solve this? This isn't a homework question but I've been running into this problem more often in multiple courses. So far...

1. describe the square root of 0 from the following perspectives: A. Algebraic B. Complex Numbers C. Limits

Hi all, Consider that one has several functions, say 3, of the form f(x,y,z) and g(x,y,z) and h(x,y,z). You know the form of these equations and they are non-linear, long, messy equations. f', g' and h' are even longer and messier and therefore assume that they cannot be found. Now...

Homework Statement \int \sqrt{t^8 + t^6 } dt Homework Equations The Attempt at a Solution I'm not sure what to do next, can someone point me in the right direction? Thank you.

"Square Root of N" Law of Random Counts According to my lab manual, "Theory says that radioactive decay obeys statistics for which the standard deviation of the counts per time interval is equal to the square root of the mean number of counts for that interval, for cases when the mean is a...

Homework Statement The average kinetic energy of a 2.35g sample of argon gas in a 7.00L container is 2.58E-22 j/atom. Homework Equations a) What is the pressure of the gas? b) What is the rot mean square velocity of teh argon atoms under these conditions? The Attempt at a Solution...

Hi, Let E = Q(a), where a is a primitive fifth root of unity. Find a basis for E as a vector space over Q, and express a/a-3 in terms of this basis. I can find a basis for E: {1, a, a^2, a^3}, but am not sure how to express a/a-3 in terms of this basis. Any help much appreciated.

From this website, http://www.analytictech.com/mb313/rootmean.htm It seems to it is more intuitive to just inverse all the sign to calculate the mean. But I can't get the idea of root mean square (equation can see here http://en.wikipedia.org/wiki/Root_mean_square) How is this idea...

I really ain't sure whether my problem is mathematical or related to Physics but i most probably think it has a mathematical solution. I am have a situation where I have subsurface seismic velocity windows at certain Depth points. In the window I have been given the two-way time in seconds...

Ok, I finally broke down and had a root canal done on my other tooth. This doctor really believes in going heavy on the local anesthetic. So much so, even my eye started to get numb, which concerned me a bit. Now I am in that gawdawful time when the anesthetic is wearing off and it feels...

I need help finding the derivative of the following equation. This may look a little messy because it involves a square root and a fraction. y = square root of: 1 + x2 / 3 + 3 - x / 5 My first thought is to change the equation to look like this: y = (1 + x2)1/2 / 3 + 3 - x / 5...

When root system is defined on some vector space V, the definition uses numbers \langle x,y\rangle = 2\frac{(x,y)}{\|y\|^2},\quad x,y\in V where (\cdot,\cdot) is the inner product. This number is handy, because a reflection of vector y with respect to a hyper plane orthogonal to x is...