Root Definition and 918 Threads

Homework Statement Find lim_{n \rightarrow \infty} \sqrt[n]{n ln(n)}. Do not use L'Hospital's Rule or Taylor Series. Homework Equations The Attempt at a Solution I suspect I need to set up some inequality for this and then apply Squeeze Theorem. But I can't find any inequality...

[SOLVED] Easy question about the root (of a real number) Hi, I'm a bit embarresed to ask this but does anybody know how to get this: \sqrt{3 - 2\sqrt{2}} = \sqrt{2} - 1 ?

Hello, I was just wondering if there is a special notation for a principal square root... I suppose using absolute value would work.. \left|\sqrt{9}\right|=+3 But it doesn't seem as fitting as an actual special square root symbol. Maybe something like this? \sqrt[+]{9}=+3 Also...

Homework Statement I wonder how to deal with the square root of Dirac Delta function, \sqrt{\delta(x)}. Actually, this comes from a problem which asking readers to calculate the wave function of a free particle and of a harmonic oscillator at time t, provided that the wave function at time...

I know that if n is odd and has k distinct prime factors, then the number of roots, x^2 = 1 (mod n), is equal to 2^k. However, I don't know how to give a formal proof to it. I simply want to bypass the generalized form x^2 = a (mod n). How can I prove it directly? Thank you.

Hello! I got the following exercise: \frac{lim}{x\rightarrow6-} {\sqrt{3x-18}} Now, since I need to evaluate the limit from the function coming from the left to the right that means that I can evaluate the function using x as a value very close to 6, but not six, right? So, since I would...

Homework Statement given the sequence {a_n} converges to A (non zero), show sqrt(a_n) = sqrt(A) Homework Equations The Attempt at a Solution I've tried to expand |sqrt(a_n) - sqrt(A)| as |a_n - A|\|sqrt(a_n) + sqrt(A)| since that gives me the numerator to work with, but I can't...

Homework Statement My prof showed us the proof that sqrt2 is not a rational number. She said, however, that we haven't proved that it is irrational, because we haven't proved that sqrt2 exists. How would we go about proving this? Homework Equations N/A The Attempt at a Solution...

Hi, the question is integrate x^2 /square root (x^2 +1). I tried to do it but i was stucked in the very last step.at the end,I got x/2 * cosh(arcsinh x) + 1/2 * arcsinh x - arcsin (square root (x^2 + 1)) +C. I dunnoe how can I simplify cosh(arcsinh x) into simplier form in term of x. I hope...

Homework Statement Can someone advice me how to solve this square root equation? n_{0}=1.5*10^{15}+\sqrt{(1.5*10^{15})^{2}+[(0.05)n_{0}]^{2}} The answer should be n0=3.0075*1015 I can't figure out how to open up the square root to solve the equation for n0. Stuck here staring at the...

Homework Statement x^2 - 1/2x - 3/16 = 0 The Attempt at a Solution Actually, I don't know where to start since I have fractions.

I am looking at the derivation for an expression that relates the concentration of an oxide to time. It appears that to do this, the author takes the limit of sqrt(A+Bt), where A and B are constants as t approaches zero and infinity. Is there an easy way to do this without making assumptions...

Homework Statement (x - 1)^2 = 4 The Attempt at a Solution This is what I've done (x - 1)^2 = 4 Everything inside parenthesis goes to: ^2 x^2 - 1^2 = 4 now we got x^2 - 1 = 4 Now (I think) I use the square root method x^2 - 1 = √4 x^2 - 1 = 2 Now I factorize: (x - 1) (x +1) = 2 This is...

Homework Statement Given f(x) = -x2 - 2x + 3, x < -1 Find f-1. Find f-1f. Homework Equations Nil. The Attempt at a Solution Actually I worked out much of the question already, and I already know that f-1f: x -> x. The problem is, I can't seem to get f-1f(x) = x on...

Homework Statement What is f'(x) of f(x) 1/sqrt(2x)? 2. The attempt at a solution In applying the problem to the derivative formula: (1 / sqrt(2(x + h)) - 1 / sqrt(2x)) / h I multiplied the problem by a special form of one but that only put the rationals on the bottom of the...

Homework Statement Find all the roots in rectangular coordinates, exhibit them as vertices of certain squares, and point out which is the principal root. The Attempt at a Solution The problem is (-8 -8\sqrt{3}i)^{\frac{1}{4}} and I found the four roots easily to be \pm(\sqrt{3} -...

Homework Statement Can someone explain to me how |-4|= \sqrt{(-4)^{2}} I'm wondering why you can't cancel out the square root sign and the square above the -4, to leave you with -4. The Attempt at a Solution I know this has something to do with the absolute value of -4, being 4, but...

The other day I was playing with my calculator and noticed that \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+...}}}} \approx 2 But, what is that kind of expression called? How does one justify that limit? And, to what number exactly does converge, for example...

Hi, While trying to simplify a solution I came up with the following sparse matrix but don't know how to solve it. [A(t)][X] = 0 $\left( \begin{array}{ccccc} A_0(t) & 1 & 1 & ... & 1 \\ A_1(t) & 1 & 0 & ... & 0 \\ ... & ... & ... & ... & ... \\ A_{n-1}(t) & 0 & ...

1.I can't figure out how the \sqrt{1+((x^2)/(4-x^2))} simplifies to 2 times\sqrt{1/(4-x^2)} I have tried rewriting it in different ways, but I can't see how it simplifies. \sqrt{x^2 + 1/4-x^2}

norm of a function ||f|| & the "root mean square" of a function. How do I explain the connection between the norm of a function ||f|| & the "root mean square" of a function. You may like to consider as an example C[0,\pi], the inner product space of continuous functions on the interval [0,\pi]...

1. \sum_{n=1}^{\infty}ntan\frac{1}{n} dont know where to start here 2. \frac{1*3*5*****(2n-1)}{n!} \frac{2n-1}{n!} \frac{2(n+1)-1}{(n+1)!}*\frac{n!}{2n-1} \frac{2n+1}{(n+1)(2n-1)} ->0 my book is showing divergence

Homework Statement \int\sqrt{40t^2+e^t^2}dt That should be e^t^2. How would I go about doing this?

(1- sqrt 3i) ^3 I am having trouble solving the sqrt 3i part. I think I need to use de moivres theorem but I am unsure. If someone could push me in the right direction that would be a massive help. Thanks.

Hi, We use as an integration form in Riemannian geometry the covariant \int \sqrt{g}d\Omega I understand how this is invariant under an arbitrary change of coordinates (both Jacobian and metric square root transformation coefficient will cancel each other), what I don't understand is why don't...

Homework Statement The Attempt at a Solution Hi, I’ve been studying Root Loci for almost 3 months now, on and off, so I know most of the methods involved with it. I’m still pretty much new to the subject still as I’ve recently hit a problem with this exercise that I’ve been working...

Homework Statement Given one root of the equation, find the others. a3-3a2+a+5=0 Given root: 2-i The Attempt at a Solution I know the answers, which are 2+i and -1. And I understand how to get the 2+i since when you square root anything, the answer can be positive or negative, but I have...

this is a strange problem easy to solve but I am having trouble understanding it intuitivly. Assume we choose a location point and name it 0. Next, in arbitrary direction and distance we place the number 1. Hence, we have created a scale(number line) that extends as much as we like. Now we...

Ok, I know this question sounds incredibly elementary, but please don't just dismiss it, try to understand what I'm REALLY asking. Ok, say we have x^{2} = 9. I know the answer is x = \pm 3. But I was just thinking about the general rule to this. I was thinking that what really happens is...

Homework Statement \int\frac{dx}{x^{1/2}-x^{1/3}} Homework Equations None The Attempt at a Solution What I did was replace \int\frac{dx}{x^{1/2}-x^{1/3}} with \int\frac{dx}{u^{3}-u^{2}} if u=x^{1/6}. Just to simplify things. And I think that was pointless. Help me out?

Root Mean Square Speed... HELP! A 11.0 cm-diameter, 24.0 cm-long cylinder contains 1.80×1022 atoms of argon at a temperature of 52.0 C. What is (Vx)rms, the rms value of the x-component of velocity? What is the rate at which atoms collide with one end of the cylinder? Determine the pressure in...

Homework Statement \int\sqrt{2*x-1} Homework Equations The Attempt at a Solution Homework Statement Obviously this can be fixed with the antiderivative of a linear function with proper constants i.e. \int A\times f(bx + c) = \frac{A}{b} F(bx + c), however my instructor provided...

Hey guys. I forget where I found this problem but it goes as follows: Prove that \sqrt[3]{2} cannot be represented in the form p+q\sqrt{r} where p,q, and r are rational numbers. It is easy to show that \sqrt[3]{2} is irrational, so it cannot be put in the form m/n, where m and n are...

can someone help me solve this question as fasd as possible?? im really headache wif it... thx~~ determine the 3 cube roots of 3-i over 3+i giving the result in modulus argument form,express the principal root in the form a+Jb

Homework Statement Find the square root of 3 - 2\sqrt 2. Homework Equations The Attempt at a Solution I don't really know how to do this quickly. Could this be done by solving x^2 = 3 - 2\sqrt 2? Or should I solve (a + b)^2 = 3 - 2\sqrt 2? By the way, the answer is 1 - \sqrt 2.

http://i42.tinypic.com/2yju26p.gif i know that the root supposed to be a distance but i can't see the distance from where to where?? the charges are not a single point i don't know how they calculate this distance ??

Homework Statement I have to design a controller for "Cruise Control System" using Root Locus method. Homework Equations We havnt studied that method yet and nor do I think it is in the course outline. Actually that is why I selected root locus so that I can learn something beyond the...

Anyone one here, knows any link where there will be a diagram of the epidermal cell of the root hair cell? If not, could you please explain to me everything about the epidermal cell of the root hair.

This has been bothering me for a while now. Without a calculator and without using "guess and check" how can find the square root of a number? For example: 6^{2} = 36 but how can you reverse it and figure out what \sqrt{36} equals? Is there some equation to it or can it only be done using guess...

I am comparing two RMS error time-series and I would like to generate error bars on the RMS results. I think the RMS error is a standard deviation of an assumed zero mean process, and I have the gut feeling that this should be the standard deviation of the sample standard deviation. Is that...

How do I find the Laurent expansion of a function containing the principal branch cut of the nth root? Example: f(z)=-iz\cdot\sqrt[4]{1-\frac{1}{z^{4}}}

I seen in some paper, there is an matrix whose element has a square root of number operator, e.g. A = \left( \begin{matrix} \alpha & \gamma \sqrt{\hat{a}\hat{a}^\dagger} \\ -\gamma \sqrt{\hat{a}^\dagger\hat{a} & \beta \end{matrix} \right) where \alpha, \beta, \gamma are real...

Homework Statement Hi, I'm stuck on the following integral. ∫ y / (√(a(y^2)-c)) dy where a and c are constants Homework Equations The Attempt at a Solution I've tried using standard integrals involving square roots in the denominator, but I'm unsure what to do with the y on...

Does x^3 - 3x + 3sqrt(3) = have a constructible root? my solution: suppose a is a constructible root of the equation above. we square both sides to get x^6 - 6x^4 + 9x^2 = 27. since a is constructible, a^2 is constructible as well and we can turn this equation into cubic poly with rational...

Homework Statement \int_0^{\infty} sin(ax) / sqrt(x) dx Homework Equations The Attempt at a Solution I thought of using integration by parts, but that gets me nowhere. I'm not sure how to go about this problem.

Is this true? n,m\in\mathbb{N} \lim_{n\to\infty}\sqrt[n]{\lim_{m\to\infty}\frac{1}{m}}=\lim_{n\to\infty}\lim_{m\to\infty}\sqrt[n]{\frac{1}{m}}=\lim_{u\to\infty}\sqrt[u]{\frac{1}{u}}=1 Thanks

hi,i read the post of sq root of 2 + sq root of 3.i understand tat i should use contradiction to solve it.yet,i stuck halfway when i tried to solve it. sq root 2 + sq root 3 = p/q 2 + 2*sq root 6 +3=p^2/q^2 5+2*sq root 6 = p^2/q^2 wat should i do after this?i hav to prove that the addition...

I was reading Roger Penrose' book "The Road to reality". He mentioned the square root of a+bi in terms of a and b. I am trying to figure his answer out for my self but am struggling. Here goes:(x+yi)^2=a+bi x^2+2xyi-y^2=a+bi x^2-y^2=a 2xy=b I can't rearrange these two equations to get x and...

Find the minimal polynomial with root 21/3 + 21/2. I would just use maple but I do not have it installed on this machine. I found the polynomial and verified that this is indeed a root. I only have Eisenstiens criterion for determining whether it is irreducible, and I can not apply it in...

Homework Statement s=k\sqrt{\frac{1+m}{1-m}} , solve for m Homework Equations The Attempt at a Solution Honestly I am stumped, but I do know there is a trick to it. I can't quite remember, but it might have something to do with taking the reciperical or the inverse...maybe the...