Difference between revisions of "LaTeX"

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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" by most, or "Lah-Tek" by some, or even "Lay-Tex) is widely used to produce well-formatted [[math|mathematical]] and scientific writing. With <math>\LaTeX</math>, it is very easy to produce expressions like
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<cmath>
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\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 } .
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</cmath> Nearly every serious student of math and science will use <math>\LaTeX</math> frequently. Through these web pages, you will learn much of what you'll need to express math and science like a pro.
  
<math>a(x+1)=3x-2</math>
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* [http://www.artofproblemsolving.com/wiki/index.php/LaTeX:LaTeX_on_AoPS Click here] to start learning how to use <math>\LaTeX</math> on AoPS
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{{Asymptote}}
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{{main|Asymptote}}
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'''Asymptote''' is a powerful vector graphics language designed for creating mathematical diagrams and figures.  It can output images in either eps or pdf format and is compatible with the standard mathematics typesetting language, [[LaTeX]].  It is also a complete programming language and has cleaner syntax than its predecessor, [http://netlib.bell-labs.com/who/hobby/MetaPost.html MetaPost], which was a language used only for two-dimensional graphics.
  
Resp:  
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Here is an example of an image that can be produced using Asymptote:
  
<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>
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<center>[[Image:Figure1.jpg]]</center>
  
<math>8</math>) Resolva a equação:
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In a sense, Asymptote is the ruler and compass of typesetting.
  
<math>\bullet</math> No papel que recebi estava assim:
 
  
<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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You can use Asymptote on the AoPSWiki right now, by enclosing the Asymptote code within <tt><nowiki><asy>...</asy></nowiki></tt> tags. For example, the following code
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<pre><nowiki><asy>
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draw((0,0)--(3,7),red);
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dot((0,0));
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dot((3,7));
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label("Produced with Asymptote "+version.VERSION,point(S),2S);
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</asy></nowiki></pre>
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created the picture
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<center><asy>
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draw((0,0)--(3,7),red);
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dot((0,0));
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dot((3,7));
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label("Produced with Asymptote "+version.VERSION,point(S),2S);
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</asy></center>
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And on the AoPS forums you can use <tt><nowiki>[asy]..[/asy]</nowiki></tt>
  
<math>\bullet</math> acho que esse sinal de menos no meio era pra ser um igual.
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Another example:
  
<math>\dfrac{1}{x-2}+\dfrac{1}{x}=\dfrac{1}{2}+\dfrac{1}{x-2}</math>
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<pre><nowiki>[asy]
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pair A,B,C,X,Y,Z;
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A = (0,0);
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B = (1,0);
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C = (0.3,0.8);
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draw(A--B--C--A);
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X = (B+C)/2;
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Y = (A+C)/2;
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Z = (A+B)/2;
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draw(A--X, red);
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draw(B--Y,red);
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draw(C--Z,red);
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[/asy]</nowiki></pre>
  
<math>\bullet</math> porém ainda fica estranho porque a solução seria <math>x=2</math>.
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<asy>
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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pair A,B,C,X,Y,Z;
 
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A = (0,0);
<math>9</math>) Resolva a equação
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B = (1,0);
 
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C = (0.3,0.8);
<math>\dfrac{1}{x-3}+\dfrac{1}{x}=\dfrac{1}{3}+\dfrac{1}{x-3}</math> em U=R-{3,0}
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draw(A--B--C--A);
 
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X = (B+C)/2;
<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.
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Y = (A+C)/2;
Portanto a questão não tem solução.
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Z = (A+B)/2;
 
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draw(A--X, red);
<math>10</math>) Resolva as equações:
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draw(B--Y,red);
 
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draw(C--Z,red);
b) <math>\dfrac{1}{a}+\dfrac{a}{a+x}=\dfrac{a+x}{ax}</math>
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</asy>
 
 
<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 00:39, 30 November 2019

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

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

Asymptote (Vector Graphics Language)
Getting Started - Basics - Drawing - Labeling - Filling - Useful functions - Examples - Macros and Packages

Help - Reference - Advanced Asymptote - 3D Graphics - CSE5 Package - How to

Main article: Asymptote

Asymptote is a powerful vector graphics language designed for creating mathematical diagrams and figures. It can output images in either eps or pdf format and is compatible with the standard mathematics typesetting language, LaTeX. It is also a complete programming language and has cleaner syntax than its predecessor, MetaPost, which was a language used only for two-dimensional graphics.

Here is an example of an image that can be produced using Asymptote:

Figure1.jpg

In a sense, Asymptote is the ruler and compass of typesetting.


You can use Asymptote on the AoPSWiki right now, by enclosing the Asymptote code within <asy>...</asy> tags. For example, the following code

<asy>
draw((0,0)--(3,7),red);
dot((0,0));
dot((3,7));
label("Produced with Asymptote "+version.VERSION,point(S),2S);
</asy>

created the picture

[asy] draw((0,0)--(3,7),red); dot((0,0)); dot((3,7)); label("Produced with Asymptote "+version.VERSION,point(S),2S); [/asy]

And on the AoPS forums you can use [asy]..[/asy]

Another example:

[asy]
pair A,B,C,X,Y,Z; 
A = (0,0);
B = (1,0);
C = (0.3,0.8);
draw(A--B--C--A);
X = (B+C)/2;
Y = (A+C)/2;
Z = (A+B)/2;
draw(A--X, red);
draw(B--Y,red);
draw(C--Z,red);
[/asy]

[asy] pair A,B,C,X,Y,Z; A = (0,0); B = (1,0); C = (0.3,0.8); draw(A--B--C--A); X = (B+C)/2; Y = (A+C)/2; Z = (A+B)/2; draw(A--X, red); draw(B--Y,red); draw(C--Z,red); [/asy]