Lebesgue point - Revision history

en>Tristessa de St Ange: Added {{ref improve}} tag to article (TW)

2014-05-12T01:26:21Z

Added {{ref improve}} tag to article (TW)

← Older revision		Revision as of 03:26, 12 May 2014
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	~~== at the foot of~~ an ~~escape Tissot appear automatically~~. ==		It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br><br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you loved this post and you would certainly such as to receive more details concerning [http://www.youtube.com/watch?v=90z1mmiwNS8 Dentists in DC] kindly see the website.

	~~Because more than enough points, even death, loss half points~~. ~~Still able~~ to ~~top 1001~~.<br><br>~~'hands now?' magic hammer staring Feng Luo.~~<br><br>~~'Yes.' Luo Feng nodded, 'Now!'<br>~~<br>~~'Haha, I'll look at, so many [http~~:~~//www~~.~~nrcil~~.~~net/fancybox/lib/rakuten_LV_46.html ルイヴィトンバッグモノグラム] talented fear~~ '~~madman' how strong~~ in the ~~end~~.~~' That magic hammer vertical face~~ with ~~eyes crazy~~.<br><br>~~Luo Feng suspended from half~~ a ~~meter, at~~ the ~~foot~~ of ~~an escape Tissot appear automatically~~.<br>On<br>~~street, two distant [http~~:~~//www~~.~~nrcil.net/fancybox/lib/rakuten_LV_16.html ルイヴィトンバッグダミエ] relative~~.~~<br><br>'Boom!' magic hammer right leg suddenly stepped~~ on the ~~ground, so that~~ the ~~ground suddenly cracked open [http://www.nrcil.net/fancybox/lib/rakuten_LV_15.html ルイヴィトンコレクション] street~~, ~~[http://www.nrcil.net/fancybox/lib/rakuten_LV_78.html ルイヴィトンデニム]~~ and ~~his whole [http://www~~.~~nrcil.net/fancybox/lib/rakuten_LV_55.html ルイヴィトンルイヴィトン] body had been before he went to Luo Feng flashed that all four arms holding~~ the ~~angular Black Hammer~~, ~~a series of lightning hit coming towards Feng Luo~~.<br><br>~~Luo Feng body floating almost backwards~~, ~~with the foot on~~ a ~~golden escape from Tissot shot, [http://www~~.~~nrcil.net/fancybox/lib/rakuten_LV_90.html ルイヴィトン財布マルチカラー]~~ and ~~then directly [http://www~~.~~nrcil.net/fancybox/lib/rakuten_LV_100.html ルイヴィトン中古品] into~~ a ~~[http://www~~.~~nrcil.net/fancybox/lib/rakuten_LV_100.html ルイヴィトン新作 2014] gold fish.<br><br>'Go!' Luo Feng eyes~~ of a ~~condensate~~.<br><br>~~golden fish swim merrily unto magic hammer~~
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	~~== 'interstellar warships~~ to ~~limit my martial arts headquarters ==~~

	~~Observation corridors~~. ~~And now it has entered~~ the ~~flood a chamber [http://www~~.~~nrcil.net/fancybox/lib/rakuten_LV_137.html 新作ルイヴィトン] which~~, ~~Luo Feng follow~~ to ~~enter~~.<br><br>~~secret [http~~:~~//www~~.~~nrcil.net/fancybox/lib/rakuten_LV_68.html ルイヴィトン長財布中古]~~ room ~~[http://www.nrcil.net/fancybox/lib/rakuten_LV_131.html ルイヴィトンショルダーバッグ] that only~~ a ~~large display~~.<br><br>~~'This is~~ a ~~damaged starship~~.~~' flood plain face, 'when I found~~ it, it ~~has been damaged and can no longer fly into~~ the ~~universe~~, ~~but ...... even if it is~~ an ~~empty shell~~ of ~~interstellar warships~~, ~~defense degree far more than any other base on Earth Municipal Building~~. '<br><br>~~'Then I have the ability~~, ~~I will get~~ it ~~out of~~ the ~~ground.'<br><br>'interstellar warships~~ to ~~limit [http://www~~.~~nrcil~~.~~net/fancybox/lib/rakuten_LV_4.html ルイヴィトンスピーディ] my [http://www~~.~~nrcil~~.~~net/fancybox/lib/rakuten_LV_137.html 新作ルイヴィトン] martial arts headquarters! Even [http://www.nrcil.net/fancybox/lib/rakuten_LV_17.html ルイヴィトンキャップ] laser cannon,~~ can ~~never expect to break interstellar warships.' Hung point display screen suddenly lights up~~ the ~~sky picture emerges~~ of the ~~universe. 'This is not our universe ...... Many ordinary people believe the Earth is so simple.'<br><br>'Our Earth humans sometimes very arrogant~~.'<br><br>'even [http://www.nrcil.net/fancybox/lib/rakuten_LV_99.html ルイヴィトンコレクション] a variety [http://www.nrcil.net/fancybox/lib/rakuten_LV_128.html ルイヴィトン最新財布] of animals on land, plant species and ~~many never noticed. ocean~~
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en>Spinningspark: Reverted edits by 188.154.99.222 (talk) to last version by Randomguess

2014-02-04T16:01:46Z

Reverted edits by 188.154.99.222 (talk) to last version by Randomguess

← Older revision		Revision as of 18:01, 4 February 2014
Line 1:		Line 1:
	~~{{Expert-subject\|date~~=~~March 2011}}~~		== at the foot of an escape Tissot appear automatically. ==
	~~{{Refimprove\|date~~=~~December 2009}}~~
	In [[mathematics]], a '''nonelementary antiderivative''' is an [[antiderivative]] for which it can be shown that there exists no formula in terms of ''[[elementary function]]s'' (i.e. involving polynomials, and the standard functions sin, cos, exp, and so on).<ref name= Weisstein>Weisstein, Eric W. [http://mathworld.wolfram.com/ElementaryFunction.html "Elementary Function."] From [[MathWorld]]--A Wolfram Web Resource. Accessed 7 Dec 2012.</ref> A [[Liouville's theorem (differential algebra)\|theorem by Liouville]] in 1835 provided the first proof that nonelementary antiderivatives exist.<ref>{{cite book\| title=The Calculus Gallery\| first=William\| last=Dunham \|isbn=978-0-691-13626-4 \|publisher=Princeton \|year=2005\| page=119}}</ref> This theorem also provides a basis for determining (with difficulty) which expressions are [[integrable]]. It can be shown that, if one is given a function of ~~any complexity, the probability that it will have~~ an ~~elementary [[antiderivative]] are very low~~.~~{{Citation needed\|date~~=~~July 2010}}~~

	~~Some examples~~ of ~~such functions are~~:		Because more than enough points, even death, loss half points. Still able to top 1001.<br><br>'hands now?' magic hammer staring Feng Luo.<br><br>'Yes.' Luo Feng nodded, 'Now!'<br><br>'Haha, I'll look at, so many [http://www.nrcil.net/fancybox/lib/rakuten_LV_46.html ルイヴィトンバッグモノグラム] talented fear 'madman' how strong in the end.' That magic hammer vertical face with eyes crazy.<br><br>Luo Feng suspended from half a meter, at the foot of an escape Tissot appear automatically.<br>On<br>street, two distant [http://www.nrcil.net/fancybox/lib/rakuten_LV_16.html ルイヴィトンバッグダミエ] relative.<br><br>'Boom!' magic hammer right leg suddenly stepped on the ground, so that the ground suddenly cracked open [http://www.nrcil.net/fancybox/lib/rakuten_LV_15.html ルイヴィトンコレクション] street, [http://www.nrcil.net/fancybox/lib/rakuten_LV_78.html ルイヴィトンデニム] and his whole [http://www.nrcil.net/fancybox/lib/rakuten_LV_55.html ルイヴィトンルイヴィトン] body had been before he went to Luo Feng flashed that all four arms holding the angular Black Hammer, a series of lightning hit coming towards Feng Luo.<br><br>Luo Feng body floating almost backwards, with the foot on a golden escape from Tissot shot, [http://www.nrcil.net/fancybox/lib/rakuten_LV_90.html ルイヴィトン財布マルチカラー] and then directly [http://www.nrcil.net/fancybox/lib/rakuten_LV_100.html ルイヴィトン中古品] into a [http://www.nrcil.net/fancybox/lib/rakuten_LV_100.html ルイヴィトン新作 2014] gold fish.<br><br>'Go!' Luo Feng eyes of a condensate.<br><br>golden fish swim merrily unto magic hammer
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	*<math>\sqrt{1 - x^4}</math><ref name= ~~Weisstein/>~~		== 'interstellar warships to limit my martial arts headquarters ==
	*<math>\ln(\ln x) \,</math>
	*<math>\frac{1}{\ln x}</math><ref>[http://www.claymath.org/programs/outreach/academy/LectureNotes05/Conrad.pdf Impossibility theorems for elementary integration;] Brian Conrad. [[Clay Mathematics Institute]]: 2005 Academy Colloquium Series. Accessed 7 Dec 2012.</ref>
	*<math>e^{e^x} \,</math>
	*<math>e^{-\frac{x^2}{2}} \,</math><ref name= ~~Weisstein/> (see [[Normal distribution]])~~

	~~The evaluation of nonelementary antiderivatives can often be done using~~ [[~~Taylor series~~]]. This is ~~because [[Analytic function\|Taylor series can~~ ''~~always'' be integrated]] as one would an ordinary [[polynomial]] (using~~ the ~~fact that any Taylor series is uniformly convergent within its radius of convergence)~~, even if ~~there~~ is ~~no elementary antiderivative~~ of ~~the function that generated the Taylor series.~~		Observation corridors. And now it has entered the flood a chamber [http://www.nrcil.net/fancybox/lib/rakuten_LV_137.html 新作ルイヴィトン] which, Luo Feng follow to enter.<br><br>secret [http://www.nrcil.net/fancybox/lib/rakuten_LV_68.html ルイヴィトン長財布中古] room [http://www.nrcil.net/fancybox/lib/rakuten_LV_131.html ルイヴィトンショルダーバッグ] that only a large display.<br><br>'This is a damaged starship.' flood plain face, 'when I found it, it has been damaged and can no longer fly into the universe, but ...... even if it is an empty shell of interstellar warships, defense degree far more than any other base on Earth Municipal Building. '<br><br>'Then I have the ability, I will get it out of the ground.'<br><br>'interstellar warships to limit [http://www.nrcil.net/fancybox/lib/rakuten_LV_4.html ルイヴィトンスピーディ] my [http://www.nrcil.net/fancybox/lib/rakuten_LV_137.html 新作ルイヴィトン] martial arts headquarters! Even [http://www.nrcil.net/fancybox/lib/rakuten_LV_17.html ルイヴィトンキャップ] laser cannon, can never expect to break interstellar warships.' Hung point display screen suddenly lights up the sky picture emerges of the universe. 'This is not our universe ...... Many ordinary people believe the Earth is so simple.'<br><br>'Our Earth humans sometimes very arrogant.'<br><br>'even [http://www.nrcil.net/fancybox/lib/rakuten_LV_99.html ルイヴィトンコレクション] a variety [http://www.nrcil.net/fancybox/lib/rakuten_LV_128.html ルイヴィトン最新財布] of animals on land, plant species and many never noticed. ocean
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	~~However~~, ~~in some cases it is not possible to rely~~ on ~~Taylor series~~. ~~For example, if the function is not ''[[infinitely differentiable]]~~'', ~~one cannot generate a Taylor series~~. ~~Even if a Taylor series can be generated, there is a good possibility that it will [[divergent series\|diverge]] and ''not~~'' ~~represent the function one is attempting~~ to ~~antidifferentiate~~. ~~Many functions which are infinitely differentiable have higher order [[derivative]]s that are unmanageable by hand~~. ~~In these cases, it is not possible to evaluate [[indefinite integral]~~]~~s, but~~ [~~[definite integral~~]~~]s can be evaluated numerically, for instance by~~ [~~[Simpson's rule~~]~~]. There are yet other cases where definite integrals can be evaluated exactly without numerical methods, but indefinite integrals cannot~~, ~~for lack of an elementary antiderivative.~~		<ul>

	~~The integrals for many of these functions~~ can ~~be written down if one allows so-called "special" (nonelementary) functions~~. ~~For example, the first example~~'~~s integral is expressible using [[Elliptic integral#Incomplete elliptic integral of~~ the ~~first kind\|incomplete elliptic integrals~~ of the ~~first kind]],~~ the ~~second and third use the [[logarithmic integral]], the fourth the [[exponential integral]], and the fifth the [[error function]]~~. ~~Still, there exist functions, such as~~ <~~math~~>~~x^x~~<~~/math~~> ~~and~~ <~~math~~>~~\sin(\sin(x))~~</~~math> for which no notation currently exists to describe their integrals (other than the use of the integrals themselves)~~.		<li>[http://www.oakleighsongs.com/cgi-bin/mojo/mojo.cgi http://www.oakleighsongs.com/cgi-bin/mojo/mojo.cgi]</li>

	~~==See also==~~		<li>[http://www.rguerra.com/cgi-bin/guestbook/guestbook.cgi http://www.rguerra.com/cgi-bin/guestbook/guestbook.cgi]</li>
	* [[List of integrals]]
	* [~~[Derivative~~]]s		<li>[http://www.rhhid.com/plus/feedback.php?aid=35 http://www.rhhid.com/plus/feedback.php?aid=35]</li>
	* [[Risch algorithm]]
	* [[Symbolic integration]]		</ul>
	* [[Algebraic function\|Algebraic]] and [[transcendental function]]s

	~~==References==~~
	<~~references/~~>
	* [http://www.~~sosmath~~.com/~~calculus~~/~~integration~~/~~fant~~/~~fant.html Integration of Nonelementary Functions], S.O~~.~~S MATHematics~~.com~~; accessed 7 Dec 2012~~.

	~~==Further reading==~~
	* Williams, Dana P., [http://www.~~math~~.~~dartmouth~~.~~edu~~/~~~dana~~/~~bookspapers~~/~~elementary~~.~~pdf NONELEMENTARY ANTIDERIVATIVES~~]~~, 1 Dec 1993. Accessed January 24, 2014.~~

	~~{{DEFAULTSORT~~:~~Nonelementary Integral}}~~
	~~[[Category~~:~~Integral calculus]~~]
	~~[[Category:Integrals]]~~

188.154.99.222: /* References */

2014-01-28T13:14:49Z

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en>SmackBot: remove Erik9bot category,outdated, tag and general fixes

2009-12-16T15:30:44Z

remove Erik9bot category,outdated, tag and general fixes

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