User:Bkell/Sandbox

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\lim_{n\to\infty}{1\over(-2)^n+1}

\sqrt{\sqrt2+2}\over2

{16\over64}={1\!{\not6}\over\not64}={1\over4}

{\sqrt{2\sqrt6+7}\over5}={\sqrt6+1\over5}

\mathbb{Z}\left[{1+\sqrt{-4\sqrt3-7}\over2}\right]

\sum\nolimits_{k=1}^n\atop{}

According to my TI-89, \int_0^{5.4}\pi(\sin^2x+1)^2\,dx=-4.24098940288 ("Warning: May not be fully simplified"). This may be because it thinks \int(1+\sin^2x)^2\,dx=\frac{19\,\mathrm{mod}(2x-\pi,2\pi)}{16}-\frac{(\sin x)(11+2\sin^2x)(\cos x)}{8}. According to the calculator, \frac{d}{dx}\left(\frac{19\,\mathrm{mod}(2x-\pi,2\pi)}{16}-\frac{(\sin x)(11+2\sin^2x)(\cos x)}{8}\right)=\left(\frac{-3\sin^2x}{4}-\frac{11}{8}\right)\cos^2x+\frac{\sin^4x}{4}+\frac{11\sin^2x}{8}+\frac{19}{8}, and apparently \left[\left(\frac{-3\sin^2x}{4}-\frac{11}{8}\right)\cos^2x+\frac{\sin^4x}{4}+\frac{11\sin^2x}{8}+\frac{19}{8}\right]-(1+\sin^2x)^2=0, so this seems to be technically correct, but there must be a bug somewhere.

The problem may be that the TI-89 claims that \frac{d}{dx}\bigl(\mathrm{mod}(x,2)\bigr)=1, which is false at even x, since mod is not continuous there.

[edit] Unspecified source for Image:Kennywood.jpg

Thanks for uploading Image:Kennywood.jpg. I notice the file's description page currently doesn't specify who created the content, so the copyright status is unclear. If you have not created this file yourself, then you need to specify who owns the copyright, please. If you got it from a website, then a link to the website where it was taken from with a restatement of that website's terms of use of its content is usually sufficient information. However, if the copyright holder is different from the website's publisher then their copyright should also be acknowledged.

As well as the source, please add a proper copyright licensing tag if the file doesn't have one already. If you created/took the picture, audio, or video then the {{GFDL-self}} tag can be used to release it under the GFDL. If you believe the media meets the criteria at Wikipedia:Fair use, use a tag such as {{Non-free fair use in|article name}} or one of the other tags listed at Wikipedia:Image copyright tags#Fair use. See Wikipedia:Image copyright tags for the full list of copyright tags that you can use.

If you have uploaded other files, consider checking that you have specified their source and tagged them, too. You can find a list of files you have uploaded by following this link. Unsourced and untagged images may be deleted one week after they have been tagged, as described on criteria for speedy deletion. If the image is copyrighted under a non-free license (per Wikipedia:Fair use) then the image will be deleted 48 hours after 19:56, 15 January 2007 (UTC). If you have any questions please ask them at the Media copyright questions page. Thank you. —Bkell (talk) 19:56, 15 January 2007 (UTC)

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