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## Limit of $x\ln{x}$

I am trying to solve $$\lim \limits_{x \to 0}x\ln{x}$$ which according to WolframAlpha (and Wikipedia) equals $0$. I managed to solve it by substituting such that $y = \dfrac{1}{x}$ and then using

mathematics

## What does "wedge" mean?

In Allen Hatcher's Algebraic Topology, $X\vee Y$ means the "wedge sum" of two (topological) spaces $X$ and $Y$. However, in $\LaTeX$, \wedge is the notation for $\wedge$, while $\vee$ is

mathematics

## Center Of Mass Troubles

I understand the concept of Center Of Mass(com), but I am having a difficult time interpreting the equation of the simplified case of one-dimension. The book I am reading defines the position of t...

physics

## How to evaluate the following limit? $\lim\limits_{x\to\infty}x\left(\frac\pi2-\arctan x\right).$

How can I evaluate this limit: $$\lim_{x\to\infty}x\left(\frac\pi2-\arctan x\right).$$ I know that the correct answer is $1$, but why?

mathematics

## Hatcher: S^2 having a CW complex of 5/6 vertices

The question is from Hatcher's Algebraic Topology Problem 2.2.24. *Suppose we build $S^2$ from a finite collection of polygons by identifying edges in pairs. Show that in the resulting CW structu

mathematics

## what does this summation mean?

I apologize if this question has been asked. I know several similar ones have been asked but I cannot find one answering this in particular. I want to know what this summation means:

mathematics

## "Job-scheduling" problem that minimizes the number of machines

In a graph, there are points that need to be visited. For each of these points, there is a certain time interval given by its start and end times, telling the time interval during which that point...

mathematics

## Euler Lagrange variational problem with $n$ independent variables and up to the hessian term

I'm trying to evaluate Euler Lagrange equation from the following relation: $$F[f(\vec{r})]=\int_{\vec{r_1}}^{\vec{r_2}} d^n r J[f(\vec{r}),\nabla f (\vec{r}),H f(\vec{r}) ]$$ where $H$ is the

mathematics

## Should words that finish with an "s" take "'s" or simply "s" to form a possessive?

For example, should I write : (1) Chris's dog OR (2) Chris' dog (1) the infants's toy OR (2) the infants' toy ? I read in Struck &amp; White (4th edition from 1979) that you shoul

english-language

## What is the radical difference between ‘this’ and ‘a’ when telling a story?

The following quotation is a line from Ron to Harry after the first stage of the Triwizard Tournament. (p359, Harry Potter 4, US edition) “You were the best, you know, no competition. Cedric di.

english-language

## Using Euler-Lagrange to find the first variational curve of

I have been working on this optimization problem for days but I cannot figure out the right way to finish it off. I am reading from Optimization Theory by Pierre, and this is problem 3.3. Note that

mathematics

mathematics

## Why can a killing vector field be determined globally by its value and first derivative at one point?

It is said in Weinberg's Book, Gravitation and Cosmology, page 377, that a killing vector field (which we a priori assume exists globally) can be uniquely determined by its value and first derivat

physics