something like MVT

by mqoi_KOLA, Mar 29, 2025, 11:37 AM

If $F$ is a continuous function on $[0,1]$ such that $F(0) = F(1)$, then there exists a $c \in (0,1)$ such that:

\[
F(c) = \frac{1}{c} \int_0^c F(x) \,dx
\]
This post has been edited 2 times. Last edited by mqoi_KOLA, 3 hours ago

IGGM - Why Monopoly Go Is So Popular Among Video Games In 2025?

by buyPOE2Currency, Mar 29, 2025, 9:14 AM

What games do you think of when you mention board games? Perhaps Monopoly Go. After the game was launched on April 11, 2023, it was loved by many gamers and developed better and better in 2024. Why can Monopoly Go stand out among many similar games till today?

At the beginning of contact with a game, players often pay attention to the artistry of the game first. I believe that everyone has played some classic board games, and their painting styles are usually realistic or gorgeous. But Monopoly Go is very different at this time. Imagine a Monopoly Man who looks like a clay man leading you through the game world. Isn’t it interesting? The scenes and props in the game are as cute as jelly, which makes people want to continue playing.

In addition, Monopoly Go breaks through the limitations of traditional Monopoly games in terms of gameplay and incorporates card games, which makes players who like to collect excited. The game official will launch the Golden Lightning event from August 7, 2024, issuing new gold cards, which makes players love and hate. How can Monopoly Go Dice collected only through daily activities satisfy their needs for decorations and stickers in the game? I think maybe buying Monopoly Go Stickers on IGGM.com can help you.

Monopoly Go Stickers have distinguishes star ratings, which prompts players to constantly look for ways to get high-star stickers, especially every time the gold stickers are updated, the shiny colors and limited time limit make many players flock to it. I have to say that the game officials understand the mentality of our players very well.

In the new year, I believe that more players will join the game Monopoly Go, and more new activities can continue to bring better experience to players.

POECurrency - What Surprises Will PoE 2 Patch 0.2.0 Bring Us?

by buyPOE2Currency, Mar 29, 2025, 8:55 AM

The trailer for PoE 2 Patch 0.2.0 has been released. The female character running in the forest with a spear has aroused many players' expectations for this update. The official release date is not far away. Perhaps players can get a glimpse of more from the known information.

This update is named Dawn of the Hunt, which is undoubtedly closely related to the launch of Huntress. The official release date is set on April 4th. Some players may be familiar with this date because it is two days after the release of Last Epoch Season 2. Developer has caused dissatisfaction among some players because they are destined to make a choice between the two games, but there are still other players who think that they don't have to succumb to the minority.

Before the release on April 4th, developer will continue to release videos and texts to promote the upcoming live broadcast on March 27th. I believe that old PoE players are already used to this move. They always announce the less important changes first to arouse the curiosity of players, and announce the most important content in real time during the live broadcast. At that time, game directors Jonathan Rogers and Mark Roberts will also answer some questions of players in the community.

PoE 2 officials will release the complete patch notes after the live broadcast. The one week between the release of this information and the official release is a good time to grasp all the information, but now players should also have a certain understanding of the content.

The protagonist in the trailer of dozens of seconds is the new class, Huntress. This is a female character who is very close to Ranger in the passive skill tree. Her spear can attack from a distance and release huge damage in close combat. Such a novel attack method must have a lot of appeal in the game, so players who want to choose and build can master more information in advance.

Secondly, many new Support Gems will be released together. Currently, there are seven known items: Perfection, Battershout, Derange, Embitter, Concoct, Commiserate, and Volcanic Eruption. They have mixed reviews among players, but this may be due to differences in preferences for different classes. In any case, they give players more choices to a certain extent.

Unique items are also an aspect that players pay close attention to. Among them, The Hammer of Faith and The Bringer of Rain have caused heated discussions in a small range. The Bringer of Rain is an item that allows a class to use a two-handed weapon with one hand. Although it has very high requirements for the attributes of the weapon, as long as you have enough PoE 2 currency, it will still be a very useful skill for you. The existence of The Hammer of Faith seems to be a way for players to choose Warrior for construction, because its ability is to provide more than 230% physical damage, but it is unknown whether players will be shaken by this.

There is still limited information about PoE 2 Patch 0.2.0, so many players have made predictions. It is said that there will be an economic reset this time. I think there must be many players who need to make up for the gap with some old players through purchases. Visiting POECurrency.com will definitely give you satisfactory results.

Maybe you haven't finished all the current game content? That doesn't affect your curiosity about Dawn of the Hunt, because it is destined to be a major change.

IGGM - Is Diablo 4 Season 8 Really An Exciting Boss Challenge?

by buyPOE2Currency, Mar 29, 2025, 7:43 AM

On March 11, the game developer released the PTR of Diablo 4 Season 8. After a week of experience, players have different opinions on the content of the new season.

Diablo 4 Season 8: Belial's Return is speculated to be officially released at the end of Season 7, that is, on April 29. Judging from the theme alone, Belial will return to Sanctuary this time. As one of the Lesser Evils in Diablo, its return will definitely bring new excitement to the game.

At present, the most obvious feeling of players about Season 8 is the upgrade of the game difficulty, which means that players will have to invest more resources in the future, such as Diablo 4 gold or Diablo 4 items. The reason why the developer did this may be that it found that players always entered the Endgame too early in previous seasons. This is particularly evident in Season of Witchcraft. It only takes an amazing nine hours for players to reach level 60! In order to change the status quo, Diablo 4 has modified the probability of item drops, and players will say goodbye to the Legendary items that were easy to obtain in the past.

In the new season, the theme of the game will change from witch power to boss power. This is a new power system. Players will collect their power by defeating 24 bosses for their own use. Each power contains Main Power and a Modifier Power. Players can use a Main Power and use three Modifier Powers to strengthen it. This will have a lot of room and possibilities for the construction of classes, and will experience a very different way of attacking than before.

In addition, Season 8 has also reset the Endgame boss fights. Lair Bosses are divided into three levels: Initiate, Greater, and Exalted. After players break through various levels, they can fight the most difficult battle with Belial, the Lord of Lies in Exalted difficulty. Although the mechanism that players need to spend special materials to summon them has been changed this time, they need to spend the corresponding Lair Key to collect the spoils of defeating the boss. This seems to be a positive change, as players only need to spend when they succeed.

Compared with the previous Helltide and Headhunts, the Apparition Incursion event, the main way for players to gain Boss power, has also changed. The changes of Boss have increased in level. After entering the event at the location marked on the map, players need to defeat the Apparition monsters first, and then defeat the Apparition Boss that you have angered. At this time, if you are lucky enough to defeat two waves of enemies, Belial will attack you as the final Boss. If your ability or equipment is not enough to resist its heavy blow, then at this time, I highly recommend you to buy Diablo 4 items on IGGM.com like me. After all, improving your equipment is the basis for victory.

Although Diablo 4 Season 8 has undergone a reform in difficulty, it has not added any additional interesting mechanisms at present, which is also a point of dissatisfaction for many players. However, there is still some time before the official release, and the specific development is still worth looking forward to.

Strange limit

by Snoop76, Mar 29, 2025, 7:42 AM

Matrix in terms of exp

by RenheMiResembleRice, Mar 29, 2025, 3:05 AM

$\begin{pmatrix}X\left(t\right)\\ Y\left(t\right)\end{pmatrix}=\begin{pmatrix}\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix}\begin{pmatrix}x\left(t\right)\\ y\left(t\right)\end{pmatrix}$

$X\left(t\right)=a_1e^t+a_2e^{-t}+a_3$
Find $a_1$, $a_2$, and $a_3$.
This post has been edited 3 times. Last edited by RenheMiResembleRice, Today at 4:05 AM

Gheorghe Țițeica 2025 Grade 12 P3

by AndreiVila, Mar 28, 2025, 10:04 PM

Let $\mathcal{P}_n$ be the set of all real monic polynomial functions of degree $n$. Prove that for any $a<b$, $$\inf_{P\in\mathcal{P}_n}\int_a^b |P(x)|\, dx >0.$$
Cristi Săvescu

Gheorghe Țițeica 2025 Grade 12 P1

by AndreiVila, Mar 28, 2025, 9:58 PM

Let $G$ be a finite group and $a\in G$ a fixed element. Define the set $$S_a=\{g\in G\mid ga\neq ag, \,ga^2=a^2g\}.$$Show that:
  1. if $g\in S_a$, then $ag^{-1}\in S_a$;
  2. $|S_a|$ is divisible by $4$.

The ratio between two integral

by Butterfly, Mar 28, 2025, 1:23 AM

Romanian National Olympiad 1999 - Grade 12 - Problem 4

by Filipjack, Jan 30, 2025, 4:01 PM

Let $A$ be an integral domain and $A[X]$ be its associated ring of polynomials. For every integer $n \ge 2$ we define the map $\varphi_n : A[X] \to A[X],$ $\varphi_n(f)=f^n$ and we assume that the set $$M= \Big\{ n \in \mathbb{Z}_{\ge 2} :  \varphi_n \mathrm{~is~an~endomorphism~of~the~ring~} A[X] \Big\}$$is nonempty.

Prove that there exists a unique prime number $p$ such that $M=\{p,p^2,p^3, \ldots\}.$

Fun with Math!

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  • Am I doing enough? Are you all expecting more from me?

    by aoum, Today at 12:31 AM

  • That's all right.

    by aoum, Yesterday at 10:46 PM

  • sorry i couldn't contribute, was working on my own blog and was sick, i'll try to contribute more

    by HacheB2031, Yesterday at 2:41 AM

  • Nice blog!
    I found it through blogroll.

    by yaxuan, Mar 26, 2025, 5:26 AM

  • How are you guys finding my blog?

    by aoum, Mar 24, 2025, 4:50 PM

  • insanely high quality!

    by clarkculus, Mar 24, 2025, 3:20 AM

  • Thanks! Happy to hear that!

    by aoum, Mar 23, 2025, 7:26 PM

  • They look really nice!

    by kamuii, Mar 23, 2025, 1:50 AM

  • I've embedded images and videos in my posts now. How do they look? (Please refrain from using my code. :noo:)

    by aoum, Mar 20, 2025, 8:58 PM

  • This is a nice blog! :)

    by charking, Mar 18, 2025, 7:48 PM

  • Are you guys actually reading my posts? Am I doing too much?

    by aoum, Mar 17, 2025, 11:35 PM

  • Thanks! Glad to hear that!

    by aoum, Mar 17, 2025, 3:07 PM

  • This is a really nice blog! One of the best I've seen on AOPS so far

    by kamuii, Mar 17, 2025, 12:13 AM

  • What does everyone think of my blog?

    by aoum, Mar 16, 2025, 10:28 PM

  • Yes, you may.

    by aoum, Mar 16, 2025, 9:00 PM

  • Can I contribute???

    by rayliu985, Mar 16, 2025, 8:00 PM

  • I'm sorry, I cannot make a post about the "performance" you mentioned, ohiorizzler1434.

    by aoum, Mar 15, 2025, 4:00 PM

  • are you a chat gpt

    by amburger, Mar 15, 2025, 1:48 AM

  • Bruh! That's crazy. can you make a post about KSI's performance of 'thick of it' at the sidemen charity football match? Personally, I thought it was amazing! KSI's energy and singing ability really made my day!

    by ohiorizzler1434, Mar 15, 2025, 1:03 AM

  • I already have a post on the Collatz Conjecture, but I'll make another, better one soon.

    by aoum, Mar 14, 2025, 10:53 PM

  • Your blog looks skibidi ohio! Please make a post about the collatz conjecture next, with a full solution!

    by ohiorizzler1434, Mar 14, 2025, 10:26 PM

  • Thanks for subscribing!

    by aoum, Mar 14, 2025, 8:24 PM

  • I get emails every post you make. Also, third post!?

    by HacheB2031, Mar 13, 2025, 11:43 PM

  • I can hardly believe you are watching my blog so carefully.

    by aoum, Mar 13, 2025, 11:42 PM

  • woah what :O two posts in 4 minutes

    by HacheB2031, Mar 13, 2025, 11:35 PM

  • I'll try. With these advanced areas, it's more likely that I'll make a mistake somewhere, so please help me out. (I will make these as accurate as I can.)

    by aoum, Mar 10, 2025, 11:51 PM

  • Maybe conic sections?

    by HacheB2031, Mar 10, 2025, 2:53 PM

  • Does anyone have some ideas for me to write about?

    by aoum, Mar 9, 2025, 10:28 PM

  • That's nice to know. I'm also learning new, interesting things on here myself, too.

    by aoum, Mar 7, 2025, 11:35 PM

  • Reading the fun facts and all from this blog's material makes me feel so at ease when using formulas. like, I finally understand the backstory of it and all that even teachers don't teach :roll:

    by expiredcraker, Mar 7, 2025, 4:50 AM

  • Thanks! There are many interesting things about math out there, and I hope to share them with you all. I'll be posting more of these!

    by aoum, Mar 7, 2025, 12:56 AM

  • Wow. This is a very interesting blog! I could really use this advice!

    by rayliu985, Mar 7, 2025, 12:43 AM

  • Thanks! Nice to hear that!

    by aoum, Mar 6, 2025, 10:56 PM

  • blog is great :) :coolspeak:

    by HacheB2031, Mar 6, 2025, 5:45 AM

  • Yes, I'll be doing problems of the day every day.

    by aoum, Mar 5, 2025, 1:15 AM

  • I think it would also be cool if you did a problem of the day every day, as I see from today's problem.

    by jocaleby1, Mar 5, 2025, 1:13 AM

  • Do you guys like my "lectures" or would you like something else?

    by aoum, Mar 4, 2025, 10:37 PM

  • Yeah, keep on making these "lectures" :)

    by jocaleby1, Mar 4, 2025, 2:41 AM

  • Thanks! Glad to hear that!

    by aoum, Mar 3, 2025, 10:28 PM

  • ME ME ME OMG I need a math mentor like this your explanation is so easy to understand! also 3rd shout! :D

    by expiredcraker, Mar 3, 2025, 3:32 AM

  • Anyone wants to contribute to my blog? Shout or give me a friend request!

    by aoum, Mar 2, 2025, 3:22 PM

  • Nice blog! Contrib?

    by jocaleby1, Mar 1, 2025, 6:43 PM

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