content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
P-Sylow subgroups, Normalizers, Indexes
August 26th 2010, 06:31 AM
adam63
P-Sylow subgroups, Normalizers, Indexes
Let G be a group.
Prove that G has no P-Sylow subgroup 'H' for which [G:N(H)]=2.
For every subgroup H in G, the Normalizer is defined as N(H):={ $g\in G: gH=Hg$ }
I need to find a way ... | 5 | [
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Rouche Theorem - Proof
October 2nd 2009, 09:44 AM #1
Super Member
Joined
Apr 2009
Posts
677
Rouche Theorem - Proof
This is a step in Rouche Theorem proof.
$f(z)$ and $g(z)$ are analytic on and inside a closed path $C$.
$|f(z) - g(z)| < |f(z)|$ for all $z$on $C$
Let $F(z) = g(z)/f(z)$
I ... | 4 | [
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Differentiation of f(x,y)
March 30th 2006, 10:26 AM
paloma
Differentiation of f(x,y)
f(x,y) = x^2 + y^2 - 3 abs(xy)
What does the vertical cross section of the surface along a diagonal through the origin (ie. the plane y = x = t) look like?
I graphed this in Scientific Workplace and got a paraboloid, b... | 5 | [
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Icon Arrangement on Desktop
up vote 32 down vote favorite
9
Story
I was bored sitting in front of my computer and using a rectangle to select icons on my screen. I could select $1$, $2$, $3$, $4$, but not $5$ icons.
(Black squares are the icons. Note that it is possible to find rectangles with $1$, $2$, $3$ ad $4$ b... | 5 | [
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0.034423828125,
-0.03... | 37,403 | 37403 | |
Properties of the n-dimensional Stereographic Projection
up vote 3 down vote favorite
1
Hello,
I'm looking for an argument that the n-dimensional stereographic projection maps circles (intersections of affine two-dimensional subspaces with S^n) to circles in R^n. I've looked around and the
only argument I saw for the... | 4 | [
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... | 37,404 | 37404 | |
Math Forum Discussions
Re: Some derivative/continuity questions
Posted: Aug 4, 2013 1:58 PM
On 08/04/2013 11:22 AM, G Patel wrote:
> On Saturday, August 3, 2013 6:51:47 PM UTC-4, phol...@gmail.com wrote:
>> On Saturday, August 3, 2013 1:37:09 PM UTC-7, G Patel wrote:
>>
>>> 1) If f is differentiable at x, is it contin... | 4 | [
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Question involving polar coordinates..
Find the area of the region that is outside the graph of the first equation nd inside the graph of the second equation. 1. r=2 2. r^2= 8sin2x (x=theta)
First, find the intersection between the circle and lemniscate: They intersect when $(2)^2=8\sin(2\theta)\implies \tfrac{1}{2}=\... | 5 | [
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Word Derangements and Arrangements
Date: 11/30/98 at 15:34:52
From: julie
Subject: Derangements
Hi Dr. Math,
I have to write this paper on derangements but I'm a little stuck.
First you have to find the arrangements on let's say a 3 letter word,
JOE. JOE has 6 arrangements: J,O,E J,E,O O,J,E O,E,J E,J,O E,O,J.... | 5 | [
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Where do I start
If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.
Nichelle14 Assume that, $r+x$ is rational. Thus, $r+x=\frac{p}{q}$ Then, $x=\frac{p}{q}-r$ But, $r$ is rational, Thus, $x$ must be rational. A contradiction. ---- Assume that, $rx$ is rational. Thus,
$rx=\fra... | 4 | [
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iagonalizable
Diagonalizable
From Conservapedia
An operator T on a finite-dimensional vector space V is diagonalizable if V has a basis of eigenvectors for T.
Denseness of diagonalizable operators
The space of complex linear operators on $\mathbb{C}^n$ may be identified with the vector space $M_n(\mathbb{C})$ of n... | 4 | [
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Parity dependent population inversion in Mordell elliptic curves
up vote 4 down vote favorite
2
I've been looking at curves of the form $y^2=x^3+k$ (where k is 6th power free and not divisible by 3^3) and I've noticed that there seems to be distinct grouping in residues classes modulo 504.
One effect that I noticed, ... | 4 | [
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Boolean algebra,isomorphism
August 16th 2012, 11:46 AM
kljoki
Boolean algebra,isomorphism
Let (B[1],+,*,^c) is Boolean algebra where B[1] is set of every positive dividers of 2310, in which are defined:x+y = lcm(x,y), x*y = gcd(x,y) and x^c = 2310/x.
Let (B[2],∩,∪,^c) is Boolean algebra of every subsets of {... | 5 | [
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Math Help
July 20th 2008, 10:38 AM #1
Junior Member
Joined
Jul 2008
Posts
51
∫ye^(y^2)
∫ye^(y^2)dy => how do I integrate this? Does it have to be done by parts?
If so, how do I need to set that up? I got about this far: u=y^2, du= 2ydy but then I'm not sure what do set dv as...
thanks for any ... | 4 | [
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Math Help
h(x)=2 squarex + 3 3 square x k(t)= 8t 3/2 g(x) 6x^5-4x^3+x^2
And the question is, find the derivative? Do you know the different rules and if so, what is the problem?
batman123 I do not understand the first two problems, they are dreadfully ambigous. Given, $6x^5-4x^3+x^2$ You need to find, (the derivativ... | 5 | [
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Calculate the volume of a sphere
June 18th 2009, 04:57 PM
arbolis
Calculate the volume of a sphere
I set up myself to calculate the volume of a sphere of radius $r$ using spherical coordinates.
I found that $V=\frac{r^2\pi}{2}$. So I think I set up badly the triple integral : $V=\int_0^{2\pi}\int_0^{\pi}\int... | 4 | [
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On polynomial functions of random variables and independence
up vote 1 down vote favorite
Suppose $Y_1, Y_2$ are independent real-valued random variables and whose distributions have a density with respect to the Lebesgue measure. Assume that all moments $\mathbb{E}Y_1^a, \mathbb{E}Y_2^b$
exist and are finite. Let $p(... | 5 | [
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Congruence Proof
May 14th 2009, 06:38 PM
wolfamdeus
Congruence Proof
If a $\equiv$ b (mod n), prove that gcd(b,n) = gcd(a,n).
I've tried working with the relationship between these equations but haven't had much luck. Thanks for any help in advance!
May 14th 2009, 08:27 PM
o_O
Let: $d_1 = \gcd (a,n) >... | 4 | [
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Stokes' Theorem
April 4th 2011, 05:52 AM
craig
Stokes' Theorem
Show, using Stokes' Theorm, that
$\oint_C \phi abla \phi \cdot \mathbf{dl} = 0$
Firstly Stokes gives us:
$\oint_C \phi abla \phi \cdot \mathbf{dl} = \int_S abla \times [\phi abla \phi] \cdot \mathbf{dS}$
Expanding $abla \times [\p... | 4 | [
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solution to f(x) = (f^(-1))(x) using quadratic equation
January 4th 2012, 08:59 PM #1
solution to f(x) = (f^(-1))(x) using quadratic equation
Alright so this is the last problem of an exercise where it has already been determined that f(x) = 4 - (x^2), x larger than or equal to 0, and (f^(-1))(x) = sqrt(4-x), x s... | 4 | [
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Limits of Indeterminate Forms and Improper Integrals
February 24th 2010, 07:28 PM #1
Junior Member
Joined
Jan 2010
Posts
28
Limits of Indeterminate Forms and Improper Integrals
Hey guys, I have a few problems I need help with and answers checked.
Problem 1. Calculate each limit.
a. $\lim_{x \to... | 5 | [
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... | 37,419 | 37419 | |
Math Help
August 11th 2009, 03:53 PM #1
Member
Joined
Jul 2009
Posts
149
derivative.
I have an equation
$y =\frac{2x-5}{(3x+2)^2}$
so i have to differentiate it.
I think i am supposed to use the quotient rule
$(\frac {f}{g})' = \frac{gf'-fg'}{g^2}$
but i am confused about g'
... | 4 | [
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... | 37,420 | 37420 | |
Probability question.
March 28th 2009, 11:24 PM
a69356
Probability question.
Hi All,
I have a question related to probability :-
Q - Ten tickets are numbered 1,2,3 ..... 10 .Six tickets are selected at random one at a time with replacement.The probablity that the largest number appearing on the selecte... | 4 | [
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rovability
Provability Logic
First published Wed Apr 2, 2003; substantive revision Tue Nov 9, 2010
Provability logic is a modal logic that is used to investigate what arithmetical theories can express in a restricted language about their provability predicates. The logic has been inspired by
developments in meta-mat... | 4 | [
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Sum of two tangent bundles of $S^{2n}$
up vote 7 down vote favorite
1
I was wondering if the sum $TS^{2n}\oplus TS^{2n}$ is a trivial bundle? The same is true for spheres of odd dimension (one can find a nowhere zero section of the second bundle, add it to the first,
the first becomes trivial and the rest of second bu... | 5 | [
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Does a power series converging everywhere on its circle of convergence define a continuous function?
up vote 45 down vote favorite
15
Consider a complex power series $\sum a_n z^n \in \mathbb C[[z]]$ with radius of convergence $0\lt r\lt\infty$ and suppose that for every $w$ with $\mid w\mid =r$ the series $\sum a_n w... | 4 | [
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Antiderivative
how do I find the antiderivative to 1 / (x(1+4x^2)) and 1/xsqrt(x+1) ?
Last edited by weasley74; April 8th 2008 at 08:31 AM.
1 / (x(1+4x^2)) the same as ( 4x^3 + x )^-1 I am in class right now (so cannot go into too much depth here) , and you may know this already, but this problem will involve the nat... | 5 | [
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Banach Fixed Point Theorem
October 16th 2009, 06:50 AM #1
Newbie
Joined
Oct 2009
Posts
5
Banach Fixed Point Theorem
How do you show that the fixed point is unique?
I would rather have hints and tips so that I can try and work through it! But I just don't know where to start!
A contraction is a ... | 4 | [
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-0.063... | 37,426 | 37426 | |
What is the equivariant cohomology of a group acting on itself by conjugation?
up vote 14 down vote favorite
11
This question makes sense for any topological group $G$, but I'd particularly like to know the answer for $G$ a compact, connected Lie group.
$G$ acts on itself by conjugation. One has the equivariant singu... | 4 | [
-0.040771484375,
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0.006103515625,
... | 37,427 | 37427 | |
Two-dimensional random walk
up vote 7 down vote favorite
1
Suppose we have a particle in the plane at the origin $(0,0)$. It moves randomly on the integer lattice $Z^2$ to any of the adjacent vertexs with equal probability $1/4$. What's the probability of
reaching a fixed point $(x,y)$ before returning to the origin?
... | 4 | [
0.059326171875,
-0.09814453125,
0.015869140625,
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0.056396484375,
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0.0284423828125,
0.09423828125,
-... | 37,428 | 37428 | |
Equivariant derived category and invariant divisor
up vote 5 down vote favorite
1
I'm looking for a reference of the following (folklore?) result.
Let $X$ be a smooth projective variety equipped with a $G=\mathbb{Z}/2\mathbb{Z}$ action (we consider the simplest case, everything can be generalized to an arbitrary fini... | 4 | [
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0.01611328125,... | 37,429 | 37429 | |
prove paraboloid is umbilic by unit vectors
April 10th 2013, 09:17 AM
heejenna55
prove paraboloid is umbilic by unit vectors
Prove that the point p=(0,0,0) on the paraboloid z= x² + y² is umbilic by computing k(û) for all unit vectors û ∈ T_p(M)
April 10th 2013, 12:41 PM
xxp9
Re: prove paraboloid is umbilic b... | 4 | [
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Parametric Equation Question
October 8th 2013, 07:03 PM
LimpSpider
Parametric Equation Question
Hi everyone!
I'm new here, and I'll like to ask for help for the following questions. Could someone please provide some general guidelines and hints on how to solve these questions but not give an answer to
t... | 4 | [
-0.0225830078125,
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-0... | 37,431 | 37431 | |
Self adjoint
December 1st 2011, 08:48 AM #1
Newbie
Joined
Oct 2011
Posts
8
Self adjoint
Hi all !!
Someone can show me if that demonstration is going right ??
Let A, B self adjoint operators such that AB = BA. Show that exist unique ortonormal base that diagonalize simultaneously A and B.
S... | 5 | [
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0.021484375,
-0.081542... | 37,432 | 37432 | |
Weil reciprocity vs Artin reciprocity
up vote 9 down vote favorite
3
This is probably an easy question for the experts:
Given two rational functions $f$, $g$ on a non-singular projective algebraic curve X (over an algebraically closed field $k$) and $p \in X$, one defines the Weil symbol $(f, g)_p$ as the value of $
... | 4 | [
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-0.01336669921875,
-0.01300048... | 37,433 | 37433 | |
Math Help
given tanΘ = 2, use trigometric identities to find the exact value of cscΘ(90°-Θ) thank you
You can observe that $\csc(90^o-\vartheta)=\sec(\vartheta)$. But if you didn't know that, how would you go about solving this problem? Note 3 things: $\sec(\varphi)=\frac{1}{\cos(\varphi)}$ $\csc(\
varphi)=\frac{1}{\... | 4 | [
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0.018066406... | 37,434 | 37434 | |
u_{xx}-u=0
December 23rd 2010, 02:22 PM
dwsmith
u_{xx}-u=0
Find the general solution to $u_{xx}-u=0$
The solution is $\displaystyle u(x,y)=f(y)e^x+g(y)e^{-x}$
How is this obtained?
Thanks.
I solved the first part:
$\displaystyle P(x)=-1\Rightarrow e^{\int P(x)dx}=e^{-\int dx}=e^{-x}$
... | 5 | [
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-0.04052734375,
-0.033935546875,
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bounds on solution of an ODE
up vote 1 down vote favorite
2
I am interested in getting a good bound for solution of the following ODE: $$ f''(t) + n^2 f(t) = (\sin(\theta t))^n$$ with the boundary condition $f(0) = f'(0) = 0$ and $t \in [0,1]$, where $\theta$
might not be an integer multiple of $\pi$ (in fact you can ... | 5 | [
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-0.033935546875,
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-0.05493... | 37,436 | 37436 | |
Area between 2 curves.
Find the area of the region R, enclosed by: x+2y=0 and x+y^2=3
I don't think you'll need to do multiple parts here. Try $\displaystyle \int_{a}^b\sqrt{3-x}-\frac{-x}{2}~dx$ where a and b are the solutions for intersection.
Have you considered how arbitrary your choice of orientation or variable... | 5 | [
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... | 37,437 | 37437 | |
Frobenius, reduction of order
November 10th 2011, 08:01 PM #1
Frobenius, reduction of order
Find the first 4 nonzero terms in a Frobenius series solution of the given differential equation. Then use the reduction of order technique to find the logarithmic term and the first 3 nonzero
terms in a second linearl... | 5 | [
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-0.0026702880859375,
-0.024658203125... | 37,438 | 37438 | |
chemical reaction....
April 4th 2011, 02:07 PM #1
Senior Member
Joined
Aug 2009
Posts
349
chemical reaction....
ok im not sure how to set this problem up
two chemicals A and B are combined to form a chemical C. the rate or velocity of the reaction is proportional to the product of the instantaneous... | 5 | [
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0.048828125,
-0.1357421875... | 37,439 | 37439 | |
Proving univariate polynomials (defined by sums, binomial coeffs, etc.) are nonnegative: is it 'routine'?
up vote 15 down vote favorite
2
My colleagues and I are working on a project related to an old paper of C. Borell and we have boiled it down to the following problem:
Show, for all integers $1 \leq i \leq k$, tha... | 5 | [
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0.09375,
-0.00405883789062... | 37,440 | 37440 | |
Tangent Passing Through a Point & Implicit Differentiation
March 5th 2011, 07:03 AM #1
Member
Joined
Mar 2010
Posts
78
Tangent Passing Through a Point & Implicit Differentiation
Question:
Find the equation(s) of the tangents to $x^2 + 4y^2 = 16$ which pass through
a) the point (2,2)
b) the po... | 5 | [
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0.0014801025390625,
-0... | 37,441 | 37441 | |
Fibonacci sequence proof
April 30th 2007, 06:16 AM #1
Junior Member
Joined
Oct 2006
Posts
43
Fibonacci sequence proof
Not sure if I'll be able to get a response in time but I'm gonna see what I can get. I have an exam in 3 hours. Even if it's not in time, I'd still like to see how to do this.
Hey I... | 4 | [
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0.... | 37,442 | 37442 | |
Getting a closed truth tree while it should be open!
September 17th 2010, 06:17 PM #1
Junior Member
Joined
Jul 2008
From
Athens, Greece
Posts
48
Getting a closed truth tree while it should be open!
Hello every one!
It is about a propositional logic problem, I have tried it vey hard maybe... cause... | 4 | [
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... | 37,443 | 37443 | |
Quadrilaterals
December 31st 2007, 11:32 AM
Sweeties
Quadrilaterals
Hello everybody, this is my first post!
How do I find the radius of a circle that is in side a diamond/ rombus? The quadrilateral has 2 diagonals of 10 and 20cm. I have got as far as finding that if you cross the diagonals you get 4
tri... | 4 | [
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0.08349609375,
-0.... | 37,444 | 37444 | |
What's algebraic approach to QM good for?
up vote 10 down vote favorite
9
The algebraic formulation of quantum mechanics (and related stuff, like quantum thermodynamics & dynamical systems etc.) via C*-algebras provides a viewpoint based mostly on abstract functional
analysis. However, I haven't really seen a working ... | 4 | [
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0.01470947265625,
0.04... | 37,445 | 37445 | |
Irreducible polynomials over ring of integers ?
November 26th 2011, 10:38 PM
princeps
Irreducible polynomials over ring of integers ?
Is it true that polynomials of the form :
$f_n= x^n+x^{n-1}+\cdots+x^{k+1}+ax^k+ax^{k-1}+\cdots+a$
where $\gcd(n+1,k+1)=1$ , $a\in \mathbb{Z^{+}}$ , $a$ is odd number , ... | 5 | [
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-0.04931640625,
-0.0... | 37,446 | 37446 | |
Is $SU(\infty)$ amenable?
up vote 7 down vote favorite
3
We can write the finitary special unitary group $SU(\infty)$ as the direct limit $\varinjlim SU(n)$ of ordinary special unitary groups. These groups $SU(n)$ are compact, thus amenable. In other words
each of them has an invariant mean (in this case, from Haar me... | 5 | [
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0.006866455078125,
-0.0146... | 37,447 | 37447 | |
How do various notions of natural transformation relate to various notions of homotopy in $2Cat$?
up vote 8 down vote favorite
6
In what follows, $2$-categories will be strict, and "$2$-functor" will mean "strict $2$-functor". (Please mention which terminological conventions you are using when answering.) I guess that... | 4 | [
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0.00714111328125,
-0.023315429687... | 37,448 | 37448 | |
Parabolic convolution of perverse sheaves in terms of the Hecke algebra
up vote 5 down vote favorite
2
It is "well-known" that the Hecke algebra $\mathcal{H}$ can be thought of as the Grothendieck group for the category of perverse sheaves on $G/B$, where the product in $\mathcal{H}$ corresponds to
convolution of shea... | 4 | [
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... | 37,449 | 37449 | |
[SOLVED] Linear transformation
April 10th 2009, 08:14 AM #1
[SOLVED] Linear transformation
Let F be the linear transformation that switches $\vec e_1 + \vec 2e_2$ for $\vec 2e_1 + \vec e_2$ and vice versa. Find the transformation matrix A for this linear transformation.
Then find the vectors $\vec f_1, \vec ... | 5 | [
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0.0299072265625,
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0.03857421875,
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-0.000766754150390625,
-0.019775390625,
... | 37,450 | 37450 | |
Problem on Finding Minimum Value - Multivariable Calculus
January 11th 2011, 09:07 AM #1
Junior Member
Joined
Jul 2008
Posts
74
Problem on Finding Minimum Value - Multivariable Calculus
Hello everyone,
I am having trouble understanding a solution to the following problem in multivariable calculus. C... | 4 | [
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-0.05224609375,
-0.0... | 37,451 | 37451 | |
Points of Symmetry and Turning Points
November 1st 2008, 08:19 PM #1
Newbie
Joined
Nov 2008
Posts
1
Points of Symmetry and Turning Points
The formula for findintg the x-coordinate of the point of symmetry of a cubic function is -b/3a. Use this formula to find the point of symmetry (x and y axes) of the f... | 4 | [
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0.09033203125,
0.07861328125,
-0.03686523437... | 37,452 | 37452 | |
Curved 3-D Object Description From Single Aerial Images Using Shadows - Patent 5943164
United States Patent: 5943164
( 1 of 1 )
United States Patent
5,943,164
Rao
August 24, 1999
Curved 3-D object description from single aerial images using shad... | 4 | [
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-0.0361328125... | 37,453 | 37453 | |
testing series for conv/div.
how do i find if a series converges/diverges for this type of series: inf Σ [(-1)^k]*[(2^k)/ln (k)] k=2
I'm wondering if you could use the ratio test for this: |an+1/an|, So you would find the an+1 term: [(-1)^(k+1)]*(2^(k+1))/ln(k+1) Now, do the ratio: [[(-1)^(k+1)]*(2^(k+1))/ln(k+1)] / [... | 5 | [
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0.0595703125,
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0.005... | 37,454 | 37454 | |
Numbers with few quadratic residues
up vote 2 down vote favorite
It is well known that the upper bound on the number of quadratic residues mod n is approximately n/2 and it reaches this bound for n prime.
Is there any similar lower bound on the number of quadratic residues mod n?
Some numerical experiments indicate ... | 4 | [
0.0185546875,
-0.0247802734375,
-0.0361328125,
-0.007049560546875,
0.08251953125,
-0.0191650390625,
0.0250244140625,
0.166015625,
-0.0027618408203125,
-0.00604248046875,
-0.06396484375,
0.0703125,
0.04833984375,
0.01544189453125,
-0.002532958984375,
-0.052734375,
0.0693359375,
-0.0... | 37,455 | 37455 | |
etale morphism and direct image
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Let $f:Y\rightarrow X$ be an etale morphism, where $X$ and $Y$ are smooth projective varieties. Let $V$ be a vector bundle over $Y$. Since $f$ is ... | 5 | [
0.00933837890625,
0.02294921875,
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0.10205078125,
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0.037353515625,
0.05322265625,
-0.041015625,
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0.00958251953125,
0.0262451171875,
-0.0654296875,
0.06005859375,
0.1328125,
0.04248046875,
-0.0181884765625,
0.046142578... | 37,456 | 37456 | |
Rate of change in a cone
November 7th 2008, 04:42 AM
Charger10
Rate of change in a cone
I am a beginner and could use help solving this problem:
water flows out of a cone shaped reservoir at 50m^3/min. the reservoir water level 6m h when full and the radius is 45m. when the water level is at 5m, (a) how fas... | 5 | [
-0.041015625,
0.0223388671875,
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0.00469970703125,
-0.03759765625,
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0.04296875,
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0.01361083984375,
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0.0260009765625,
0.0830078125,
-0.0283203125,
0.041259765625,
-0.08837890625,
0.0522460937... | 37,457 | 37457 | |
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Topic: linear algebra with inverse of matrix.
Replies: 3 ... | 5 | [
-0.1162109375,
0.04248046875,
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0.080078125,
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0.0771484375,
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0.06640625,
-0.0341796875,
... | 37,458 | 37458 | |
equation of tangent plane to a surface
March 3rd 2011, 12:57 AM #1
Junior Member
Joined
Oct 2010
Posts
39
equation of tangent plane to a surface
I managed to do the first part okay ---- said some stuff about 3x^2 and y^2 term, its not linear etc..
but Im stuck in the part in red. Is it supposed... | 4 | [
-0.02587890625,
-0.029052734375,
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0.033935546875,
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0.0703125,
0.033447265625,
-0.0244140625,
0.06103515625,
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-0.0289306640625,
0.00159454345703125,
-0.06494140625,
0.0167236328125,
-0.10107421875,
-0... | 37,459 | 37459 | |
Integrating a function that's proportional to...
April 12th 2008, 09:43 PM
Boris B
Integrating a function that's proportional to...
I am supposed to integrate a function that is proportional to
$(10+x)^{-2}$
My initial strategy was to treat that as the reciprocal of
$x^2 + 20x + 100$
but that lea... | 5 | [
-0.0250244140625,
0.0225830078125,
0.07177734375,
0.01171875,
0.031982421875,
-0.032470703125,
-0.0277099609375,
0.0230712890625,
-0.031494140625,
0.05419921875,
0.16015625,
0.0419921875,
0.02783203125,
0.1162109375,
-0.0751953125,
-0.000804901123046875,
0.083984375,
0.03857421875,... | 37,460 | 37460 | |
Splines
May 12th 2011, 03:57 PM
Sogan
Splines
Hello,
i try to solve this problem:
Let $a=x_0 < x_1 <...<x_n =b$ be a partition of [a,b]. and let $V={v \in C^0[a,b] : v_{|[a,b]} \in C^4[x_i-1,x_i]$ with $v(x_i)=y_i$for some $y_i \in \mathbb{R}$. Show that every solution of
$argmin_{v \in V} \int |v... | 5 | [
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0.02978515625,
-0.032958984375,
-0.0091552734375,
-0.042724609375,
0.0771484375,
-0.0216064453125,
-0.06... | 37,461 | 37461 | |
Latex Help Needed
August 19th 2008, 09:42 PM #1
Latex Help Needed
Hey Guys I need help turning this into LATEX, I have tried at it for a good portion of the night but cant seem to find the correct combination.
Here is what I have so far if anyone would like to correct it.
10.(\frac{(x+8)^2}{x^4})^{-3... | 4 | [
-0.00701904296875,
0.0703125,
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0.0230712890625,
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0.059814453125,
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0.12060546875,
-0.022705078125,
0.0098266... | 37,462 | 37462 | |
Cauchy-Schwarz inequality for Integrals
January 16th 2009, 12:24 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Cauchy-Schwarz inequality for Integrals
Suppose that the functions $f,g,f^2,g^2, fg$ are integrable on the closed, bounded interval [a,b]. Prove that:
$\int ^b _a fg \leq \sqrt ... | 5 | [
0.03076171875,
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0.064453125,
0.03564453125,
0.023681640625,
-0.045654296... | 37,463 | 37463 | |
Differential forms with poles on the diagonal
up vote 2 down vote favorite
1
This question arises because I'm reading Frenkel and Ben Zvi's book "vertex algebras and algebraic curves" at the moment.
Let $X$ be a curve, $\Delta \subset X \times X$ the usual diagonal embedding, and $\mathcal{O}$ the sheaf of functions ... | 4 | [
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0.0625,
0.0255126953125,
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0.042236328125,
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-0.0213623046875,
-0.013671875,
... | 37,464 | 37464 | |
SAMPLE SIZE
Very frequently asked question in statistical consulting is, how large should the sample size be to estimate a mean?
The answer will depend on the variation associated with the random variable under observation. The statistician could correctly respond, only one item is needed, provided that the standard d... | 5 | [
0.047607421875,
0.0771484375,
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0.140625,
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-0.0291748046875,
-0.02783203125,
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0.029541015625,
0.0196533203125,
... | 37,465 | 37465 | |
Discrete Proof! HELP!
Prove that if one root of $ax^2+bx+c=0$ is rational, then both are rational.
You know that solution of a quadratic equation follows the quadratic formula. Then assume that one of the roots is rational, and not complex, so sqrt(b^2-4ac) is a rational number. Then show that the
other root must also... | 4 | [
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0.1259765625,
-0.00946044921875,
0.032470703125,
0.0517578125,... | 37,466 | 37466 | |
Practical use of Calculus
July 23rd 2006, 08:42 PM #1
Newbie
Joined
Jul 2006
From
Cape Town, RSA
Posts
17
15.1
A rectangular container has the following dimensions (cm)
Length $3x$
Width $90-3x$
depth $\frac{x}{3}$
Determine
15.1.1 Volume V in terms of $x$
15.1.2 The val... | 5 | [
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0.0966796875,
0.00836181640625,
0.02978515625,
0.08007812... | 37,467 | 37467 | |
complicated equation
January 5th 2011, 07:31 AM #1
Junior Member
Joined
Dec 2010
Posts
52
complicated equation
need help with this one :/
2^(3-x) = 2^x - 2
2^(3-x) - 2^x + 2 = 0 = 2^-x * 2 * 2 * 2 - 2^x + 2
someone who can help with the rest ?
$2^{3-x}=2^x-2\;\Leftrightarrow\;\dfrac{2... | 4 | [
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0.02099609375,
0.050537109375,
0.019775390625,
-0.00921630859375,
-0.043701... | 37,468 | 37468 | |
Application of Haar Wavelets and Method of Moments for Computing Performance Characteristics of Electromagnetic Materials
Vishwa Nath Maurya^1, , Avadhesh Kumar Maurya^2
^1Department of Mathematics, School of Science & Technology, University of Fiji, Fiji Ex-Professor & Director, Vision Institute of Technology, U.P. ... | 4 | [
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-0.024169921875,
-0.0810546875,
0.0306396484375,
0.0174560546875,
-0.0483... | 37,469 | 37469 | |
Volumes by Cylinderical Shells
February 24th 2009, 12:30 PM #1
Junior Member
Joined
Feb 2009
Posts
30
Volumes by Cylinderical Shells
Find the volumes of the solids generated by revolving the regions about the given axes.
The region bounded by y= square root x y= (x^2)/8
a.) the x-axis
b.) th... | 5 | [
0.054443359375,
0.0615234375,
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0.0615234375,
-0.0016021728515625,
0.0216064453125,
0.0269775390625,
-0.... | 37,470 | 37470 | |
Getting stuck on series - can't develop Taylor series.
October 4th 2010, 03:55 AM
liquidFuzz
Getting stuck on series - can't develop Taylor series.
$\frac{Log z}{sin(\pi z)}$ Find convergences radius at z = 1 and develop a Taylor series.
Just by looking at the function I see that deviser and numerator has z... | 5 | [
0.01153564453125,
-0.02978515625,
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0.08935546875,
0.0380859375,
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0.07177734375,
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0.07373046875,
-0.0654296875,
-0.04931640625,
-0.0264892578125,
-0.08984... | 37,471 | 37471 | |
Square Roots by Hand
Instructions: Example:
1 Count the number of digits your number has that are on the left 28.6, breaks up into
side of the decimal point. If the number of digits is... | 4 | [
0.012939453125,
0.02294921875,
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0.05419921875,
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-0.04541015625,
-0.062255859375,
0.... | 37,472 | 37472 | |
Algebra 2 - write the equation of the parabola in vertex form? Help!
January 2nd 2013, 09:42 AM
wakefuldoze
Algebra 2 - write the equation of the parabola in vertex form? Help!
Hi I'm new to this forum! I'm in Algebra 2 and I have a midterm to take tomorrow and I really need help with this problem!
It says:... | 4 | [
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0.09228515625,
-0.0341796875,
-0.0874... | 37,473 | 37473 | |
Algebraic surfaces of general type
up vote 3 down vote favorite
Question. Are there smooth complex surfaces of general type with an irregularity $q = 1$ and Euler characteristic $3$.
If the answer is yes, what is known about the geometry of such surfaces? Are there some explicit constructions?
ag.algebraic-geometry ... | 5 | [
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0.002029... | 37,474 | 37474 | |
Derivatives involving both product/quotient rule
December 6th 2009, 08:33 AM #1
Member
Joined
Oct 2009
Posts
229
Derivatives involving both product/quotient rule
Find f'(x) for y = (x+5 / x+1) (2x+1)
I don't know how to proceed here. Do I use the quotient rule inside the first brackets? Then what?
... | 5 | [
-0.08740234375,
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0.109375,
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0.004730224609375,
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0.02880859375,
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0.01031494140625,
0.0120849609375,
0.0625,
-0.01348876953125,
0.... | 37,475 | 37475 | |
[SOLVED] Physics - Projectile Motion (2d), Vectors
January 29th 2010, 07:16 PM
lightningstab714
[SOLVED] Physics - Projectile Motion (2d), Vectors
Problem: A projectile is fired in such a way that its horizontal range is equal to 14 times its maximum height. What is the angle of projection?
The work I have... | 4 | [
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0.09765625,
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0.0225830078125,
0.00714111328125,
0.... | 37,476 | 37476 | |
Value of Angle DBC
Associated Topics || Dr. Math Home || Search Dr. Math
Value of Angle DBC
Date: 1/23/96 at 21:3... | 4 | [
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0.1171875,
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0.014404296875,
-0.072265625,
-0.01806640... | 37,477 | 37477 | |
Question about limits
March 21st 2010, 07:49 AM #1
Newbie
Joined
Mar 2010
Posts
13
Question about limits
In part (a) of my questions I'm asked to show $\lim_{n \rightarrow{\infty}}[\frac{1}{n-1}]^\frac{1}{n} = 1$
I have done this, and part (b) asks me to consider a sequence of functions
$f_n : ... | 5 | [
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0.01171875,
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0.03... | 37,478 | 37478 | |
Power Series Solutions of linear DE
March 18th 2010, 11:52 AM #1
Newbie
Joined
Oct 2009
Posts
22
Power Series Solutions of linear DE
Without actually solving the DE, find a lower bound for the radius of convergence of power series solutions about the ordinary points x=0 and x=1
DE: (x^2+25)y''+2xy'+... | 5 | [
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0.0137939453125,
-0.0... | 37,479 | 37479 | |
Area bounded by curves(check answer)
September 22nd 2008, 02:54 PM
javax
Area bounded by curves(check answer)
Hello.
Calculate the area bounded by these curves:
$y=-x^2+4x-3$
$y=4x-3$
$x=2$
My answer is $\frac{77}{12}$ . I went like this:
For the area above x
$S_1 = \int\limits_{\fra... | 5 | [
0.0458984375,
-0.036376953125,
-0.0140380859375,
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-0.01373291015625,
0.05712890625,
-0.04956... | 37,480 | 37480 | |
Integrals
July 28th 2008, 11:40 AM #76
Now this is one of the ones that I am most proud of
$\int_0^{\infty}\ln\left(\frac{e^x+1}{e^x-1}\right)~dx$
First let
$\ln(u)=x$
$\Rightarrow{\frac{du}{u}=dx}$
And we can see that
$0\mapsto{1}$
$\infty\mapsto\infty$
So we get
$=\int... | 5 | [
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0.00811767578125,
-0.09814453125,
... | 37,481 | 37481 | |
I want to explain the latest steps from this Q
Hi I want to explain the latest steps from this Q
What does $50 - 20$ equal? Edit: Your actual working out seems a bit backward. You are trying to use the identity $\tan{(\alpha - \beta)} = \frac{\tan{\alpha} - \tan{\beta}}{1 + \tan{\alpha}\tan{\
beta}}$ to simplify $\fra... | 4 | [
0.027099609375,
0.083984375,
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0.1259765625,
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0.0712890625,
-0.08056640625,
0.1162109375,... | 37,482 | 37482 | |
Interpolation with Polynomials and Splines
Introduction
First of all, take a look here, where Tobias von Petersdorff has published his interpolation form written in Java.
Have you tried to find some sample code written in C# that helps you to draw a Spline? I've tried with no success.
This is a port of his sample pr... | 4 | [
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continued fraction expansion help, / proof
October 22nd 2013, 02:22 AM
Tweety
continued fraction expansion help, / proof
I have attached the question I need help, question 5, and really not sure how to go about,
any help / tips appreciated
thank you
October 22nd 2013, 06:24 AM
SlipEternal
Re: conti... | 4 | [
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Projectiles question
June 5th 2011, 08:01 AM #1
Projectiles question
Gun in a fortress can can shoot missiles from a velocity of √(2gk).Gun is situated "h" meters high from the sea level.How to show that maximum horizontal range of a missile sent by the gun is 2√
[k(k+h)] ?
I did this ,but not even close... | 4 | [
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0.0225830078125,
0.049560546875,
-0.0033721923... | 37,485 | 37485 | |
Finding all roots of a polynomial
up vote 6 down vote favorite
3
Is it possible, for an arbitrary polynomial in one variable with integer coefficients, to determine the roots of the polynomial in the Complex Field to arbitrary accuracy? When I was looking into
this, I found some papers on homotopy continuation that se... | 5 | [
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0.... | 37,486 | 37486 | |
The Schrödinger Equation - Corrections
[
Click here for a PDF of this post with nicer formatting
]
In my
last post
, I claimed
Additionally, we can extend from here that any quantum operator $\mathcal{G}$ is written in terms of its classical counterpart $G$ by $\mathcal{G}=-i G/\hbar.$
Peeter Joot correctly
... | 4 | [
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0.0... | 37,487 | 37487 | |
Non-Exact Equation - Integrating Factor
October 10th 2010, 02:08 PM #1
Member
Joined
Mar 2009
From
Alberta
Posts
173
Non-Exact Equation - Integrating Factor
Hey I've got a question here where I need to find an integrating factor to make an equation exact, but it's in two variables and I'm having trou... | 4 | [
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0.0390625,
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0.0072021484375,
-... | 37,488 | 37488 | |
Integration Question
How do you integrate an equation in the form of $\int$$\sqrt{x^2+a^2}$$dx$
Various ways to go about it. A nice tangent substitution appears to be called for at first glance. What have you tried?
I was actually using cos and sin, but i didnt get anywhere. I dont see how I can use tan
$x = a\cdot\... | 5 | [
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0.0517578125,
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0.0228271484375,
0.0059... | 37,489 | 37489 | |
Intersection of all normalizers
up vote 3 down vote favorite
1
This is probably standard for group-theorists: Let $G$ be a finite group. Is it true that the intersection of all normalizers of subgroups equals the center? If so, where do I find a proof? What
about the same question for infinite groups?
The original qu... | 5 | [
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0.... | 37,490 | 37490 | |
Question on Limits
June 28th 2008, 08:40 AM #1
Member
Joined
Apr 2008
Posts
123
Question on Limits
Find lim as x-->0+ for x^(tan x).
It seems to suggest 0^0 = 1, but when I apply L'Hopital's I get 0 instead. Help would be great
edit: sorry missed out the minus sign, should be 0 instead of infin... | 5 | [
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... | 37,491 | 37491 | |
information on an Euler product
up vote 5 down vote favorite
1
The following Euler product came up in some sieving applications: $f(z, s) = \prod_{\mbox{primes}} \left(1-\frac{z}{p^s}\right).$
What is known about this function? (Analytic continuation? Asymptotics?) This must be quite classical...
nt.number-theory cv... | 4 | [
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0.01806640625,
-0.064941406... | 37,492 | 37492 | |
What is the Hirzebruch-Riemann-Roch formula for the flag variety of a Lie algebra?
up vote 20 down vote favorite
23
If we have a finite dimensional Lie algebra g, then the flag variety of g is a projective scheme.
My question is what is Hirzebruch-Riemann-Roch formula for this projective scheme? Are there any interes... | 5 | [
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Newton Methods
WOLFRAM LANGUAGE TUTORIAL
Gauss–Newton Methods
For minimization problems for which the objective function is a sum of squares,
it is often advantageous to use the special structure of the problem. Time and effort can be saved by computing the residual function , and its derivative, the Jacobian . The ... | 4 | [
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0.0625,
-0.041748046875,... | 37,494 | 37494 | |
Surfaces in a 3-manifold with the same Gaussian curvature with respect to two ambient conformal metrics
up vote 9 down vote favorite
1
Let $M$ be a 3-smooth manifold and $g_{1}$ and $g_{2}$ two conformal metrics on $M$. Consider an immersed surface S in $M$ and let $K_{1}$ and $K_{2}$ be the Gaussian curvatures of $... | 4 | [
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0.002426147460937... | 37,495 | 37495 | |
Equivariant cohomology of finite group actions and invariant cohomology classes
up vote 2 down vote favorite
Let $W$ be a finite group acting on a space $X$. In what generality is it true that $H^*_W(X) = H^* (X)^W$? We always have a map $H^*_W(X) \rightarrow H^* (X)^W$, but it is certainly not an
isomorphism with $\m... | 5 | [
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The center of a circle through three points - Math Central
While the first section of this response is simplest, it is less precise than the second approach.
Hi Gary.
First, I'd simplify the problem by dropping the redundant data and putting the origin of the graph at N 43, 30 min and W 96, 45 min. Then you have thre... | 5 | [
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Application of AM-GM? It's not quite so simple...
September 13th 2007, 05:54 AM #1
Newbie
Joined
Sep 2007
Posts
5
Application of AM-GM? It's not quite so simple...
Let
a; b; c be positive reals such that abc = 1. Prove that
{1/sqrt(b + a/2 + 1/2)} + {1/sqrt(c + b/2 + 1/2)} + {1/sqrt(a + c/2 + 1... | 5 | [
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0.05712890625... | 37,498 | 37498 | |
Help with exponential problem.
February 28th 2009, 12:53 PM
Murphie
Help with exponential problem.
I could use some help understanding these problems and setting up the equation using the formulas.
problem:
A single-celled amoeba doubles every 4 days. How long would it take one amoeba to produce a popula... | 5 | [
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-0.0... | 37,499 | 37499 |