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Roblox is a game-making platform and community where players can create their own games, play, and share with each other. Simply select a game, choose a character, place, and map, invite friends, and you are ready to go! By combining the infinite possibilities of its programming language, Lua, with the abundant content already available on the site, players can create all of the games that their imagination can conceive. Players can build their own stories, game modes, characters, and game worlds and even share their creations with each other via user-generated content. In addition to in-game game creation, players can invite their friends and post publicly for others to play and rate. At its core, Roblox is a game. It is a place to go to play games with friends and create new adventures.
History:
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Roblox was created in 2004 by David Baszucki and Erik Cassel. Although it initially started as a text-based roleplaying game in which players were content to just talk and type to one another, in 2005 the platform was redesigned to let users create games in real-time with a variety of different genres (including action, adventure, racing, and simulation) and with visual and auditory components.
The platform was officially launched on September 15, 2006 with only a dozen games available. Roblox launched out of beta in January 2007 with its first online distribution of a game called “Bunny Blox”. Roblox’s growth trajectory was not steady, but steady, until roughly the time of its initial public offering in 2013. Since 2013, Roblox has seen a notable expansion in its user base, the breadth of its genre offering, and the number of games available daily.
The game changed its interface to a fully immersive 3D user interface in the summer of 2013. At this time, it was the third-most-viewed website on Facebook, beating large social media and gaming sites like YouTube and Zynga. In addition to giving players a new interface and enabling them to create a virtual world, this change doubled the audience size of the company. On July 31, 2015, Roblox opened up its software development kit, allowing developers to create games for the platform in their own forums.
Roblox Viewer:
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Roblox Viewer allows players to play uploaded games on the platform. In May 2014, Roblox Viewer was released for desktop computers, adding a

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Subscribe to this channel and learn more about how to get free Robux.Q:

Show that $\sqrt{x}$ is an improper integral.

This is my attempt so far:
$$\int_{0}^{\infty}\sqrt{x}\,dx
ot\mathop{\longrightarrow}\limits^{u=\sqrt{x}}_{0} u^2\cdot dx=u^2\cdot 2\sqrt{x}\;\;\;\text{as $u\to\infty$.}$$
I am thinking that $\displaystyle\int_{0}^{\infty}\sqrt{x}\,dx=\lim_{u\to\infty}\int_{0}^{\infty}\sqrt{u^2}\,du=\lim_{u\to\infty}u\int_{0}^{\infty}1\,du=\lim_{u\to\infty}u=\infty$.

A:

By the mean value theorem you get
$$\int_0^{\infty} \sqrt x \,dx = \frac{1}{2} \int_0^{\infty} \frac{dx}{\sqrt x}=\frac{1}{2} \lim_{t \to 0^+} \int_0^t 1 \,dx=\frac{1}{2}\lim_{t \to 0^+} \frac{t}{2}=\infty$$

A:

The fact that we have $\sqrt x$ is not the same as $x^{1/2}$, they are actually different. The thing is that $0^2=0$. This is a problem that we have to live with when dealing with differentials, $dx$ is really not the same as $\sqrt x$, it’s actually
$$\sqrt x dx = \sqrt x \cdot 2\cdot x^{ -1/2} \, dx$$
and the integrals of both sides are equal, but the limits of integration are different. The way we solve this is by interpreting $\sqrt x \, dx = \sqrt x \cdot dx$ as the integral of $\sqrt x$ and say that this is
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