Root Definition and 918 Threads

Homework Statement Example: If the tension in a string is 25N, the square root of that tension would be 5 ...what?

Homework Statement I don't have the problem in front of me but it was something like "converge or diverge"?: \sum 5^n/(n+1) The Attempt at a Solution I would like to know that if I use the root test, would I get lim n-> \infty 5/(n+1)^1/n = 5/(n+1)^0 = 5/1 = 5 ? I suspect...

Homework Statement 9y'' + 6y' + y = 0 r^2 + 6r + 1 ( -6 +/- root 36 - 36 ) / 18 lamda = -6/18 = -(2/9) mu = 0 (this is the part I am unsure about, because if i end up with a zero under the root, then does this make the final equation into this: y = c_1*cos(0*x) +...

Homework Statement Hi, I have a problem in my book in which they use a method of making sqrt( 36 + x^2 ) a perfect square by simply making x = 3( t - 1/t ) and then we get 9( t + 1/t )^2 by substituting back into sqrt(36 + x^2). My question is that why did the chose 3( t - 1/t ), is...

Homework Statement Using the Newton raphson method with x0=6, find the root of x2- 2 to 3dp. Then estimate the number of iterations the bisection method that would be required to achieve the same accuracy. Homework Equations The Attempt at a Solution I have done the first...

Find six distanct sixth roots of -1 + i root 3 I want check my answer ==== > x = -1 y = root 3 r = 2 tan Q = 2pi/3 -1 + i roo3 = 2 { cos ( 2 pi / 3 ) + i sin 2 pi / 3 ) = 2 e ^2 pi i / 3 } now six root -1 + i roo3 = 2^1/6 e ( 2 pi/3...

Show that sq. root of 2 to power sq. root of 2 to ... N converges Sq. root of 2^sq root of 2 ^ sq. of 2...N Use monotonous convergence theorem to that it converges and determine what it converges to.

Homework Statement find the square root of: 4+4(sqrt3)i put the answer in a+bi form Homework Equations finding the nth roots: √(r(cos(theta)+isin(theta)))=√r(cos(theta+2(pi)(k)/(n))+isin(theta+2(pi)(k)/(n) where k=0,1 The Attempt at a Solution first i converted my...

I have some measurements from a physics lab experiment and I am coding in Matlab a fit for the data. [Note this is not a problem with Matlab, my problem here is theory] In normal regression of statistics the RMSE is given by: s=\frac{\sigma}{\sqrt{n}} =\sqrt{\frac{\Sigma (\epsilon...

My notes claim that the square root loop \sigma : S^1 \longrightarrow RP^1 ; z=\cos 2\pi t +i\sin 2\pi t \longrightarrow [\cos \pi t, \sin \pi t] is a homeomorphism, where [x,y] is an equivalence class given by the antipodal equivalence relation on the circle. However, this map doesn't even...

Using the root test find whether the series converges or diverges: Lim Sin (4/(3n+3)) / Sin (4/(3n)) n-> inf. I have no idea how to cancel out the sin terms

Homework Statement Let n be a nonzero integer and let a be an integer with gcd(a, n) = 1. We have two equivalent conditions which characterize primitive roots: (i) a is primitive modulo n if the order of a is \phi(n). (ii) a is primitive modulo n if for every element b with gcd(b, n) = 1 we...

Question is pretty simple : How do I know that square root 3/2 = 0.8660 or how can 0.8660 be converted into square root 3/2 more importantly. My calculator is out of style so it displays only numbers. Thanks

Homework Statement The matrix C is self-adjoint and positive definite on \mathbb{ C}^2. Determine \sqrt{\mathbb{C}} \in \mathbb{ C}^{2x2} . C=\left(\begin{array}{cc}5&-4i\\4i&5\end{array}\right) The Attempt at a Solution Characteristic polynomial: (5-\lambda)^2 - 16 = 0 What I...

Homework Statement Determine whether the series converges or diverges. \sum (\sqrt {k} - \sqrt {k - 1})^k Homework Equations The Attempt at a Solution (a_k)^\frac{1}{k} = \sqrt{k} - \sqrt{k - 1} What do I do here..? = \frac{1}{\sqrt{k} + \sqrt{k-1}} \to 0 ?

I have no idea how to go about this, except that we are supposed to use proof by contradiction to show that the square root of 3 is an irrational number. Any help or tips is appreciated. Thanks.

Homework Statement solve for x: [ x / sqrt(x^2 + h^2) ] = [ d / sqrt(d^2 + h^2) ] I need to solve for x. Homework Equations sq rt * sq rt = what is inside the square root square both sides of an equation The Attempt at a Solution Can anyone help me remember how to get...

Hello all, I'm attempting to find in literature a method of determining from a Lie algebra's full root system in an arbitrary basis which roots are simple. It seems there are many books, articles, etc on getting all the roots from the simple roots but none that go the other way. My task is...

I've struggled for days reading about square roots of complex numbers and I get most of the problems but not this one. I really want to understand what is going on in this problem, hope someone can help! 1. The complex number (C) is C = 1/\sqrt{i*x} . find the two roots of C. The solution...

Homework Statement Maclaurin series for square root (1+x) Homework Equations The Attempt at a Solution I attempted to find the maclaurin series for the function Square root of 1+x. F(0)=1 first term= 1 F'(0)=1/2 second term= (1/2)x F''(0)=-1/4 Third term (-1/4)x^2...

hi there, I'm trying to plot r against \phi by solving the following ODEs using runge-kutta. The problem I'm having is with the square root. How do I know when it will be positive and when it will be negative? If this is a simple question I apologise I'm not that great with the maths :). E and...

Let ∑ak be a series with positive terms. Ratio test: Suppose ak+1/ak -> c. If c<1, then ∑ak converges. If c>1, then ∑ak diverges. If c=1, the test is inconclusive. What if ak+1/ak diverges (i.e. ak+1/ak->∞)? Do we count this as falling into the case c>1? Can we say whether ∑ak converges...

I came across this weird graph from another thread: y=\left(x^2-6x+8+\sqrt{x^4-12x^3+52x^2-96x+64}\right)^2 It seems that there is a root y=0 for the domain x=[2,4]. I've never seen such weird behaviour on a graph before. How could analysis of this function (or not?) determine that there...

Homework Statement \int dx/(e^{x}\sqrt{1-e^{-2x}}) Homework Equations The Attempt at a Solution I have absolutely no idea of how to start the problem, any help is greatly appreciated! thanks!

Consider square root of 4. Can square root of 4 be +2 or -2? I asked that to my math teacher so he said: NO, square root of 4 is +2! But I can't really understand why it cannot be -2 since -2 squared is also 4. One thing I've imagined is: square root of 4 can be +2 or -2, but for...

Homework Statement This isn't really a homework question, but I was considering a different model of library fines... where the fine at the end of the 1st late day is $0.01, and it increases geometrically with a common ratio of 2, so it goes like $0.01, $0.03, $0.07, $0.15... Then I...

Homework Statement Does it converge or diverge? Sum n=0 to infinity : (n/(n+1))^(n^2) The attempt at a solution I know I need to use the root test. But what I get is ... Limit to infinity : (n/(n+1))^n It seems that the n/(n+1) would go to 1 because when you multiply the top...

Hello, I came across the following formula after asking for practical applications of math in finance and other sciences, it concerns mortgage payments A = Pi/1-(1+i)^-n The above denominator end part reads (1+i)^(-n) As a mathematical question, is it possible to rearrange the...

hi there, i have written a small program in C++ and if the user puts in the wrong values for some of the variables the operation will end up trying to square root a negative number and this returns that the answer is not a number can anyone show me how to write an if function that if...

1. Homework Statement [/b] i have this thing: 2u\sqrt{}um is this expression the same as: 2u^3/2*m^1/2 Homework Equations The Attempt at a Solution

Homework Statement Find the linerization of square root of sin(2x) Homework Equations The Attempt at a Solution I don't even know how to start. What is linearization? Thanks

Homework Statement Evaluate lim x->8 (x-8)/(cubed root of x) -2) Homework Equations The Attempt at a Solution I multiplied both numerator and denominator by (cubed root of x) +2. In the denominator, I wrote it as ((x^1/3)-2)*((x^1/3)+2) which simplifies to (x^2/3)-4. I have...

Homework Statement http://img37.imageshack.us/img37/1237/63391287.jpg Homework Equations $\displaystyle \Large \int udv$ = uv - $\displaystyle \Large \int vdu$The Attempt at a Solution can i take this 3 out of the integral as well and make it 3/8 *$\displaystyle \Large \int _0^8 sqrt(64 +...

root mean square current?? Homework Statement A) If the voltage across the outlet terminals in your house is 110 Vrms at 60 Hz, and an ideal 5 H inductor is placed across the outlet terminals, what is the magnitude of the rms current flowing through the inductor? B) Assuming that the 110...

Homework Statement Does it converge, and what is the sum: \sum_{n=1}^{\infty}\frac{1}{n n^{\frac{1}{n}}} Homework Equations The Attempt at a Solution Please check my method and conclusion: Using the root test: \displaystyle\lim_{n\to\infty}\left|\frac{1}{n...

Homework Statement why is it possible to take the cube root of a negative number and not a square root of a negative number? Homework Equations The Attempt at a Solution

Homework Statement (x-7)^2=(x+3)^2 2. The attempt at a solution I squared both sides and received x-7=x+3 However, that cannot be correct because the variables cancel out which means there is no solution. The book shows that there is a solution of 2

Homework Statement Find the Integral of \sqrt{sin(x)} Homework Equations none The Attempt at a Solution People say it's -2/3cos(x)^{3/2} which I don't think so or is it? thank you

calculate the RMS (root mean square) of this function. the period T=4 the formula is V_{rms}=\sqrt{\frac{1}{T}\int_{0}^{T}V_r^2dt} V_{rms}=\frac{1}{4}4\int_{0}^{T}(4t)^2dt} V_rms=\sqrt{s}=\sqrt{\frac{16}{3}} the solution says that they divide the graph into 4 traingles and they sum their areas...

Problem Calculating a limit with a square root, I'm stuck :( Homework Statement The limit is equation 9-t / 3-sqrt(t) as t approaches 9 I'm stuck on the how to simplify this? Thanks for any help. Homework Equations The Attempt at a Solution

Suppose I am looking for the root of a function of the form: f(x)=x ^{m}-c, where c,m>1. Suppose I take my first guess to be x _{0}=c. Then using Newtons method my next guess will be given by: x _{n+1}=x _{n} - \frac {f(x _{n})}{f'(x _{n})}. From this, or thinking about this...

Homework Statement show that \sqrt{1+ja} is equivalent to \pm(1+j)(a/2)^{1/2} with a>>1 Homework Equations Euler's formula? The Attempt at a Solution with a>>1 |z| = \sqrt{(1 + a^{2})} == a lim a-->infinity arctan (a/1) == \pi/2 \sqrt{z} = \sqrt{(ae^{j\pi/2})} \sqrt{z} =...

I was thinking on the square root of 2 being irrational proof... and I got the idea that you could use the same idea for every root higher than two. The cube root, the quartic root, the quintic root, etcetera. (Obviously assuming the roots are natural numbers.) As a reassurance I'm not crazy...

I was wondering why it is that when the temperature of something is being described, the root mean square speed of its atoms is used and not simply the mean speed. Why is the RMS more meaningful/useful when describing these things than the mean? Thanks.

Homework Statement Hi again all, I've just managed to prove the existence (non-constructively) of a 'square root function' f on some open epsilon-ball about the identity matrix 'I' such that [f(A)]^2=A\qquad \forall\, A \,\text{ s.t.}\, \|I-A\|<\epsilon within Mn, the space of n*n matrices...

Homework Statement At 318 K and 1.04 x 10-2 atm, the density of a gas is 1.75 x 10-5 g/cm3. (a) Find vrms for the gas molecules. (b) Find the molar mass of the gas. Homework Equations vrms= sqrt (3RT/M) pV=nRT pM=dRT pV=(m/M)RT The Attempt at a Solution the main problem i...

Hello, For 1 and 2 I want to calculate rms then x_{rms}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}x_i^2}\Rightarrow x_{1,2}=\sqrt{\frac{1}{2}(1^2+2^2)}=\sqrt{\frac{5}{2}} And also x_{rms}=\sqrt{\frac{1}{x_2-x_1}\int_{x_1}^{x_2}f^2(x)dx} For the function f(x)=x, x_1=1, x_2=2...

Could someone help me with this? I feel it should likely be easy, but I'm baffled anyway: Homework Statement Prove the validity of the limit lim x -> x_0 sqrt(x) = sqrt(x_0) Homework Equations use definition of limitThe Attempt at a Solution Generally confused. I start with |sqrtx - sqrtx0|...

Homework Statement Use Euler's formula to write 2^{1-i} in the form a+ib. The Attempt at a Solution I know this has to be so simple because I could do this easy if the question was to write e^{1-i} in the form a+ib using Euler's. So what I do not understand is how does 1-i being...

Does anyone know how to solve for x in the following equation: x + \sqrt{x} = 6 I don't know how to solve for x with eq'ns like this, and I'm studying inverse fxns right now, so I'm told that's what I'm supposed to do. The square root sign is throwing me off. The first time I tried...