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Difference between revisions of "LaTeX"

(Undo revision 32970 by Klismann (Talk))
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<math>5</math>)Resolva em U=R, onde a incógnita é x e <math>a\neq3</math>  
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{{Latex}}
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The <math>\LaTeX</math> typesetting system (pronounced "Lay-Tek" or "Lah-Tek") is widely used to produce well-formatted [[math|mathematical]] and scientific writing. With LaTeX, it is very easy to produce expressions like
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<cmath> \sqrt{\frac {a^2+b^2+c^2}3} \geq \frac {a+b+c}3 \geq \sqrt[3]{abc} \geq \frac 3 { \frac 1a + \frac 1b + \frac 1c } . </cmath>
  
<math>a(x+1)=3x-2</math>
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You can ask questions about <math>\LaTeX</math> on the <url>index.php?f=123 LaTeX Forum</url>, and you can test your skills in the <url>index.php?f=224 Test Forum</url>.
  
Resp:
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Nearly every serious student of math and science will use LaTeX frequently. Through these web pages, you will learn much of what you'll need to express math and science like a pro.
  
<math>ax+a=3x-2 \to ax-3x=-(2+a) \to x=\dfrac{-(2+a)}{a-3} \to x=\dfrac{(2+a)}{3-a}</math>
 
  
<math>8</math>) Resolva a equação:
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== See also ==
  
<math>\bullet</math> No papel que recebi estava assim:
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* [[Asymptote: About | Asymptote]] (graphics language for LaTeX)
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* [[LaTeX:About |More About LaTeX]]
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* [[LaTeX:Downloads|Setting up LaTeX]]
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* [[LaTeX:Basics|LaTeX Basics]]
  
<math>\dfrac{1}{x-2}+\dfrac{1}{x}-\dfrac{1}{2}+\dfrac{1}{x-2}</math> em U=R-{2,0}
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== External links ==
 
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* [http://tug.ctan.org TUG], the TeX User Group
<math>\bullet</math> acho que esse sinal de menos no meio era pra ser um igual.
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* [http://en.wikipedia.org/wiki/LaTeX Wikipedia Article]
 
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* [http://www.latex-project.org/ The LaTeX Project Site]
<math>\dfrac{1}{x-2}+\dfrac{1}{x}=\dfrac{1}{2}+\dfrac{1}{x-2}</math>
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* [http://www.artofproblemsolving.com/LaTeX/AoPS_L_TeXer.php This] is a useful script that will change LaTeX input into a transparent image.
 
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* [http://dev.baywifi.com/latex/ An online LaTeX compiler]
<math>\bullet</math> porém ainda fica estranho porque a solução seria <math>x=2</math>.
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* [http://nirvana.informatik.uni-halle.de/~thuering/php/latex-online/latex.php Another online compiler]
Não pode ser <math>x=2</math> porque a questão pede todas as soluções menos o 2 e o 0.Assim acredito que a questão não tenha solução.
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* [http://www.verbosus.com A free, browser based latex editor]
 
 
<math>9</math>) Resolva a equação
 
 
 
<math>\dfrac{1}{x-3}+\dfrac{1}{x}=\dfrac{1}{3}+\dfrac{1}{x-3}</math> em U=R-{3,0}
 
 
 
<math>\bullet</math> Da mesma forma que ocorreu na questão anterior a solução seria <math>x=3</math>, porém a questão pede todas as soluções menos o 3 e o 0.
 
Portanto a questão não tem solução.
 
 
 
<math>10</math>) Resolva as equações:
 
 
 
b) <math>\dfrac{1}{a}+\dfrac{a}{a+x}=\dfrac{a+x}{ax}</math>
 
 
 
<math>\bullet</math> Ele deveria ter mencionado quem era incógnita e quem era constante. Pelas outras questões supomos que x seja a incógnita.
 
 
 
<math>\bullet</math> Ele também não mencionou que o 'a' e o 'x' tem que ser diferente de 0.
 
 
 
<math>\bullet</math> Considerando o que foi dito acima, vem:
 
 
 
<math>\dfrac{1}{a}+\dfrac{a}{a+x}=\dfrac{a+x}{ax}</math> <math>\to</math> <math>\dfrac{a+x+a^2}{a(a+x)}=\dfrac{a+x}{ax}</math> <math>\to</math> <math>xa+x^2+a^2x=(a+x)^2</math> <math>\to</math>
 
 
 
<math>xa+x^2+a^2x=a^2+x^2+2ax</math> <math>\to</math> <math>a^2x+ax-2ax-a^2=0</math> <math>\to</math> <math>a^2x-ax-a^2=0</math> <math>\to</math> <math>(a^2-a)x=a^2</math> <math>\to</math> <math>x=\dfrac{a^2}{a^2-a}</math> <math>\to</math> <math>x=\dfrac{a}{a-1}</math>
 
 
 
d) <math>\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{8}{x-1}</math> <math>\to</math> <math>\dfrac{x+1}{x-1}-\dfrac{8}{x-1}=\dfrac{x-1}{x+1}</math> <math>\to</math> <math>\dfrac{x-7}{x-1}=\dfrac{x-1}{x+1}</math> <math>\to</math>
 
 
 
<math>(x-7)(x+1)=(x-1)^2</math> <math>\to</math> <math>x^2+x-7x-7=x^2+1-2x</math> <math>\to</math> <math>-6x-7=1-2x</math> <math>\to</math> <math>x=-2</math>
 
 
 
Não tenho certeza se o que eu fiz está certo.
 

Revision as of 16:58, 23 November 2009

LaTeX
About - Getting Started - Diagrams - Symbols - Downloads - Basics - Math - Examples - Pictures - Layout - Commands - Packages - Help

The $\LaTeX$ typesetting system (pronounced "Lay-Tek" or "Lah-Tek") is widely used to produce well-formatted mathematical and scientific writing. With LaTeX, it is very easy to produce expressions like \[\sqrt{\frac {a^2+b^2+c^2}3} \geq \frac {a+b+c}3 \geq \sqrt[3]{abc} \geq \frac 3 { \frac 1a + \frac 1b + \frac 1c } .\]

You can ask questions about $\LaTeX$ on the <url>index.php?f=123 LaTeX Forum</url>, and you can test your skills in the <url>index.php?f=224 Test Forum</url>.

Nearly every serious student of math and science will use LaTeX frequently. Through these web pages, you will learn much of what you'll need to express math and science like a pro.


See also

External links

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