mailing-list for TeXmacs Users

[Anderson Brasil da Silva <address@concealed>]

Hi. I am using TeXmacs 2.1.5 (the appImage version) at linux mint 22.1. 
For some reason, when exporting to the PDF format, documents with 
pictures appears really small. I am attaching an example at this e-mail 
(just compare the size of the geometric picture at page 8 at the TM file 
and at the PDF file). Is it a known issue? Is there a solution?

Thanks in advance,

Anderson Brasil

Attachment: prova1ParaAutoAvaliacaoVersaoPuramenteConvertidaParaPDFPeloTexmacsSemEdicaoPosterior.pdf
Description: Adobe PDF document

<TeXmacs|2.1.5>

<style|<tuple|article|portuguese|old-spacing|old-dots|old-lengths>>

<\body>
  <\small>
    <\with|font-series|bold>
      Disciplina: Fundamentos da Matemática

      Professor: Anderson Brasil

      Turma: Licenciatura em Matemática

      Nome:___________________________________

      \;

      Avaliação de 16/09/2026 (simulação para auto-avaliação)
    </with>

    \;

    <\em>
      Esta avaliação vale dez pontos, e terá a duração de 120 minutos. Nada a
      respeito de números pares, além de sua definição, deverá ser admitido
      como previamente conhecido e utilizado sem demonstração.
    </em>
  </small>

  <vspace*|1fn>1) [1,0 pt] Prove que <math|a<rsup|8>+7a<rsup|4>+2\<gtr\>4a<rsup|2><around*|(|a<rsup|4>+1|)>,\<forall\>a\<in\>\<bbb-R\>>.
  DICA: Comece escrevendo que <math|<around*|(|a<rsup|2>-1|)><rsup|4>\<geqslant\>0>.

  \;

  <page-break*>2) [1,0 pt] Um número real <math|x> é dito <em|ridículo>
  quando <math|x<rsup|4>\<leqslant\>2+x<rsup|2>>. Mostre <em|rigorosamente>
  que <math|<sqrt|2>> é ridículo.

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  3) [1,0 pt] O número <math|0> é um número par? Justifique
  <em|rigorosamente>, a partir da definição algébrica que adotamos.

  \;

  <page-break*>4) [1,0 pt] Seja <math|n> um número natural. Um número real
  <math|\<alpha\>> é dito um <em|grampeador na base <math|n>> quando existe
  algum número natural <math|m> tal que <math|\<mathe\><rsup|m>=\<alpha\><rsup|n>>.
  Prove <em|rigorosamente> que <math|<sqrt|\<mathe\>>> é um <em|grampeador na
  base <math|4>>.

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  \;

  5) [1,0 pt] Um número <math|x\<in\>\<bbb-R\>> é dito um <em|pardal> quando

  <\equation*>
    \<exists\>a,b\<in\>\<bbb-Q\><rsup|\<ast\>><rsub|+><left|\|>x=a+<sqrt|b>.
  </equation*>

  <yes-indent>Prove <em|rigorosamente> que <math|3> é um pardal.

  <page-break*>6) [1,0 pt] Um número <math|x\<in\>\<bbb-R\>> é dito um
  <em|semipardal> quando

  <\equation*>
    \<exists\>a,b\<in\>\<bbb-Q\><rsup|\<ast\>><rsub|+><left|\|>x=<sqrt|a>+<sqrt|b>.
  </equation*>

  Prove <em|rigorosamente> que <math|<sqrt|2+<sqrt|3>>> é um semipardal.

  \;

  <page-break*>7) [1,0 pt] Dizemos que dois números reais <math|x> e <math|y>
  formam um <em|par 2-algébrico> quando existirem polinômios reais <math|p> e
  <math|q>, ambos não constantes e de coeficientes inteiros, tais que
  <math|p<around*|(|x|)>+q<around*|(|y|)>=0>. Prove <em|rigorosamente> que
  <math|0> e <math|2> formam um par 2-algébrico.

  \;

  <page-break*>8) [1,0 pt] Utilize diretamente a definição de números pares
  para provar <em|rigorosamente> que se <math|a,b> e <math|c> são números
  pares, então <math|a+b-c> é um número par.

  \;

  <page-break*>9) [1,0 pt] Utilize diretamente a definição de números pares
  para provar <em|rigorosamente> que se <math|n> é um número par, então
  <math|<frac|<around*|(|n<rsup|>+6|)><rsup|2>|2>> é um número par.

  \;

  <page-break*>10) [1,0 pt] Escreva a área do quadrado BCDE (figura
  <reference|FiguraSegundaDemoPitagoras>) de duas formas diferentes para
  fazer uma segunda demonstração para o teorema de Pitágoras. OBS: Por
  simplicidade, não será exigido aqui que se justifique que os triângulos são
  congruentes ou que as figuras que parecem quadrados são efetivamente
  quadrados. Assuma que tudo é o que parece ser.

  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