To Tukulti-Ninurta, say thus, Abbashi-Bidathyur says, I asked you for twenty oxen and fourteen pots of beer to be sent to Ur, so why haven't you sent them?
user19161
@RajeshD And why are you still typing the space before the ? bro?
@JasperLoy To tell you the truth, the first chapter of The Art of Computer Programming, in which some section is named after Mathematical Preliminaries, really confused me a lot.
Yesterday I was so bored that I decided to go to a random theatre and watch any movie that is playing there, too my luck it was Spiderman (the amazing) (just released that day). Its a good movie
Question: I want to learn knowledge about intergration and infinity series first, so can I only take an overview of applications of differentiation in geometry?
Any advice?
It seems that the applications of differentiation in geometry is not being interesting me a lot.
So I wonder whether it is important for me to prepare to learn the preceding topic: integration, infinity series.
integration, infinite series and sequences and calculus you will obviously get a good grip on them with ease. What do you mean by differentiation in Geometry?
I found that $D$ could be dense on $\Bbb R$. For example, $D=\Bbb Q$, and $f(x)=0$ when $x\not\in\Bbb Q$, and $f(x)=1/q$ when $x=p/q$, $q>0$ and $p\perp q$.
Now what do you mean by more dense, or almost/everywhere, If "for all x_o" means it is dense everywhere. for some $x_o$ means well its not dense oevr entire set but there are places where it is dense
Let $L$ be the set of all functions $f\colon [0,1]\to\mathbb R$ that have the property that $\lim_{x\to a} f(x)$ exists for all $a \in [0, 1]$. Show that:
(i) $L$ is a vector space. Each $f \in L$ is bounded.
(ii) For each $f \in L$, define $f^c(x): = \lim_{y\to x} f(y)$ ($x \in [0, 1]$). $f^c$ is continuous.
(iii) '$f^c =0$' is equivalent to 'there exist $x_1, x_2, \dots$ in $[0,1]$ and $a_1, a_2,\dots$ in $U$ with $\lim_{n\to\infty} a_n = 0$, such that $f(x_n) = a_n$ for every $n$, and $f=0$ elsewhere'.
(iv) Describe the general form of an element of $L$. Show that every $f\in L$ is Riemann integrable.
Does anyone have any intuitive explanation for fix-point iteration? I know what it is and I understand it. But I want to give some friends of mine a good exploitation =)
Coxeter came to Cambridge and gave a lecture [in which he stated a] problem for which he gave proofs for selected examples, and he asked for a unified proof. I left the lecture room thinking. As I was walking through Cambridge, suddenly the idea hit me, but it hit me while I was inthe middle of the road. When the idea hit me I stopped and a large truck ran into me....
So I pretended that Coxeter had calculated the difficulty of this problem so precisely that he knew that I would get the solution just in the middle of the road.... Ever since, I’ve called that theorem “the murder weapon.” One consequence of it is that in a group if $a^2=b^3=c^5=(abc)^{-1}$, then $c^{610}=1$.
it's amazing how banal, mechanistic symbolic things like group presentations and diophantine equations can easily get very complicated, and even undecidability rears its head
First, we extend $[0..1]$ to $\Bbb R$ as this way: for $x_0<0$, we have $f(x_0)=\lim_{x\to0^+}f(x)$, and for $x_0>1$, we have $f(x_0)=\lim_{x\to1^-}f(x)$.
Perhaps it is matter of taste, but I would consider the function written as $$f'(x)=\begin{cases} \ldots & x<0 \\ \ldots & x\in(0,1) \end{cases}$$ nicer.
You have $f'(x)=-2xf(x)$ for $x<0$.
You can simplify it for the remaining cases, too.
What is the exercise asking to do BTW. Just to calculate the derivative?
@MartinSleziak Nope, ty study the entire fuction.. I got: Domain, Simmetry, Intersection with x=0 and y = 0, Asymptotes, and now I'm trying to do the first derivative
