Is $$\dfrac{x^2 + 2x}{x}$$ a polynomial?
Is $\frac{x^2+x}{x+1}$ a polynomial?  Fist question can be: on which field/ring or etc? In basic, let's take over $\mathbb R$.  Actually, it is $x$ if $x \ne -1$.  Can we say again it is a polynomial, or a near-polynomial or what?   Can we say it is a polynomial over $\mathbb R - \{-1\}$? But there is structure here for $\mathbb R-\{-1\}$.  This question can be academically, not sure, but I want to ask it in the level of primary school, then academically.
What are the primary differences between the rules of D&D 3.5 and Pathfinder? What are some of the rule changes that Pathfinder brings in comparison to D&amp;D 3.5?  I am curious what changes were made so I can explain to my group what it has to offer. Position of \caption gets counter incremented twice Force figure placement in text Does a (half) beheaded Ettin take bleeding damage of some sort? Let's say a character cuts off one of an Ettin's heads, but the other head is still intact, and it's as such still alive. Obviously, there's a lot of blood. Does the Ettin take continuous damage from naturally bleeding out? Or does it not work that way? If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$ What is the probability that a person is the second person to roll a 6 for the first time? Suppose $A$, $B$, and $C$ roll a die in turns. What is the probability that $A$ is the second person to roll a $6$ for the first time? Glossaries: Make a glossary entry recognizable in printing How do you make it visible to the reader that the printed word/term is an entry in the glossary? In my PDF on the computer, I just see it because I use the hyperref package and there's a red box around it. But when printing it, there's just nothing that makes it visible to the user.  Is there a typographically good and common way of doing this? Why are only certain shutter speeds or apertures available? How to split a file according to a column (including header) and rename the generated files? I have a .txt that can be exemplified like this:  NAME | CODE name1 | 001 name2 | 001 name3 | 002 name4 | 003 name5 | 003 name6 | 003   I need to write a script to split this file according to the CODE column, so in this case I'd get this:  file 1: NAME | CODE name1 | 001 name2 | 001  file 2: NAME | CODE name3 | 002  file 3: NAME | CODE name4 | 003 name5 | 003 name6 | 003   According to some research, using awk would work:  $ awk -F, '{print &gt; $2".txt"}' inputfile   The thing is, I also need to include the header to the first line and I need the file names to be different. Instead of 001.txt, for example, I need the file name to be something like FILE_$FILENAME_IDK.txt. Both sides differentiation expression with integral I have a problem with derivation of some function. This is related to computing the Poincare Map of Logistic Population model with Periodic harvesting. This function is:  $\phi(t,x_0) = x_0 + \int_{0}^{t} f(s,\phi(s,x_0)) ds $,  where $\phi(t,x_0)$ is a function: $\mathbb{R}  \times \mathbb{R} \rightarrow \mathbb{R}$.  I'm trying to differentiate  equation of this function both sides  with respect to $x_{0}$. In book from this equation comes from the result of this differentiation is:  $\frac{\partial \phi}{\partial x_0} (t,x_0) = 1 + \int_0^{t} \frac{\partial f}{\partial x_0} (s, \phi(s,x_0)) \cdot \frac{\partial \phi}{\partial x_0} (s, x_0)ds$.  I can't understand expression under the integral. In this book it is explained that it is clear from chain rule.Could someone explain to me this transformation in easy way? I will be grateful for your help Best regards ascending/descending in LINQ - can one change the order via parameter? One click to site meta? Right now from a main site, it takes TWO CLICKS to get to http://meta.SITE.stackexchange.com/ - ONE!  TWO!    Why not ONE click on the &quot;Hot Meta Posts&quot; &amp; &quot;Featured On Meta&quot; - How can I find the program I'm hiding in bash Favicon of Earth Science and Spanish are too similar (exactly the same in HNQ list) The favicon is used in various places around the Stack Exchange (SE) network, to identify the site. Currently, Earth Science has  for main and  for meta. The problem I see is that these are awfully similar (i.e. exactly the same, as demonstrated here) to those for Spanish.SE, which are  for main and  for meta. The larger versions offer slight differences, but it's still hard to tell quickly which is which. Power users on this site, did you guess right, even after some time to think about it? (Answers under spoiler tag).   for main and  for meta.  for main and  for meta.    The first one is Earth Science and the second is Spanish.  Should SE visually distinguish between the two very different sites? XSD extend a complex type From : In calculus and other branches of mathematical analysis, an indeterminate form is an algebraic expression obtained in the context of limits. Limits involving algebraic operations are often performed by replacing subexpressions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is known as an indeterminate form.    The indeterminate forms include $0^{0},\frac{0}{0},(\infty - \infty),1^{\infty}, \ \text{etc}\cdots$   My question is can anyone give me a nice explanation of why $1^{\infty}$ is considered to be an indeterminate form? Because, i don't see any justification of this fact. I am still perplexed. how to calculate $$\int_0^\infty \frac{x^{3}}{e^{x}-1} \; dx$$   Be $q:= e^{z}-1 , p:= z^{3}$ , then $e^{z} = 1 $ if $z= 2\pi n i $, so the residue at 0 is : $$\frac{p(z_{0})}{q&#39;(z_{0})} = 2\pi i n ^{3}$$  problem is that this is not symmetric, so how does one find the definite integral? Summing up the area on a polygon by a certain attribute result I wish to know if there's a tool on QGIS equivalent to the Excel's "SUMIF".    I have a shapefile of a land use and cover that's classified by the attribute with the name of the classes, for example: "vegetation", "urban centers" and "pastures". My goal is to calculate the area of each class, but since it's composed by various polygons, I need to add up all the areas from all polygons that were put in the same class.  Like I mentioned in the beginning of the question, I know that Excel has a function that can do such thing for me, but it turns out that the sum made by excel doesn't match the area's total given by QGIS.  English is not my first language, so if the explanation isn't clear enough, I'll be glad to rephrase it. Expansion of $(1+\sqrt{2})^n$ Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$ Let $\{ a_n, n\geq 1\}$ be a sub-additive sequence, i.e. for any $m,p\geq 1$ $$ a_{m+p} \leq a_m + a_p. $$ .Prove that $$\lim_{n\to\infty} \frac{a_n}{n} = \inf_n \frac{a_n}{n}.$$ I guess the first step is to state $$a_{n} = a_{mp+q} \leq a_{mp} + a_q$$ but I'm not sure where to go from here....