{"id":6785,"date":"2015-06-14T23:48:21","date_gmt":"2015-06-14T21:48:21","guid":{"rendered":"https:\/\/kamerpower.com\/?p=6785"},"modified":"2025-08-11T00:21:59","modified_gmt":"2025-08-10T23:21:59","slug":"epreuves-concours-iut-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee\/","title":{"rendered":"Epreuves concours IUT Douala Mathematiques 2011 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2011"},"content":{"rendered":"

R\u00c9PUBLIQUE DU CAMEROUN
\nCONCOURS D\u2019ENTREE EN 1\u00e8re ANN\u00c9E
\nSession de juillet 2011<\/span>\u00a0IUT<\/strong>\u00a0de l\u2019Universit\u00e9
\nde\u00a0Douala\u00a0Fili\u00e8re: PFTIN-<\/strong>GI<\/strong>
\n\u00c9preuve de Math\u00e9matiques<\/strong><\/a>
\nDUREE : 3\u00a0HEURES\u00a0KA<\/span>M<\/span>ER<\/span>POWER<\/span>.COM
\n<\/span><\/p>\n

Epreuves concours IUT Douala\u00a0Mathematiques
\n**********<\/span>*********************<\/span><\/span><\/span><\/h3>\n

<\/span>Epreuves concours IUT Douala Mathematiques<\/a> 2011 PFTIN-GI<\/span><\/span><\/h3>\n

<\/span>Exercice I\u00a0<\/span><\/strong><\/span><\/h3>\n

1)<\/strong> Soit f une fonction r\u00e9elle d\u2019une variable r\u00e9elle d\u00e9finie par:
\nf (x ) = e2x<\/sup>\u00a0\u2212 4ex<\/sup>\u00a0+ 3<\/p>\n

    \n
  1. Determiner le domaine de definition de f et calculer ses limites.<\/li>\n
  2. Dresser le tableau de variation de f .<\/li>\n
  3. R\u00e9soudre l\u2019equation f(x ) = 0.<\/li>\n
  4. En d\u00e9duire le signe de f.<\/li>\n<\/ol>\n

    2)\u00a0<\/strong>Soit g une fonction r\u00e9elle d\u2019une variable r\u00e9elle d\u00e9finie par:<\/p>\n

    g(x ) = ln(e2x<\/sup>\u00a0\u2212 4ex<\/sup>\u00a0+ 3)<\/p>\n

      \n
    1. Determiner le domaine de d ?finition de g et calculer ses limites.<\/li>\n
    2. Dresser le tableau de variation de g .<\/li>\n
    3. Montrer que g(x ) se met sous la forme g(x ) = 2x + h(x ) ou h est une
      \nfonction qui tend vers 0\u00a0quand x tend vers +\u221e<\/li>\n
    4. Que peut on en deduire ?<\/li>\n
    5. Calculer g(\u22121)et g(2) puis tracer soigneusement la courbe de g.<\/li>\n<\/ol>\n

      <\/span>Exercice II<\/span><\/strong><\/span><\/h3>\n

      Soit P(z ) = 4z4<\/sup>\u00a0+ 4(cos \u03b1)\u03bbz2<\/sup>\u00a0+ \u03bb2<\/sup>\u00a0ou \u03bb = 1 + cos \u03b1 ,\u03b1 \u2208 [0; \u03c0]<\/span><\/p>\n

        \n
      1. Exprimer P(x) avec x = (2\/\u03bb)z2<\/sup><\/span><\/li>\n
      2. Determiner en fonction \u03b1,le module et argument de chacun des nombres\u00a0complexes x1\u00a0et x2\u00a0qui sont les racines de l\u2019equation P(x) = 0.<\/span>
        \n3. En d\u00e9duire en fonction \u03b1,le module et argument de chacun des nombres\u00a0complexes z1, z2, z3\u00a0et z4\u00a0qui sont les racines de l\u2019equation P(z) = 0.<\/span><\/li>\n<\/ol>\n

        Exercice III<\/span><\/strong><\/p>\n

        \"Exercice<\/p>\n

        Soient (Un) et (Vn) deux suites d\u00e9finies par:<\/span><\/p>\n

          \n
        1. Montrer que la suite(Vn) est g\u00e9om\u00e9trique et preciser sa raison.<\/span><\/li>\n
        2. Exprimer ()\u00a0et ()\u00a0en fonction de n<\/span><\/li>\n
        3. La suite()\u00a0est elle convergente ?<\/span><\/li>\n
        4. Calculer la limite de ln() \u00a0quand n tend vers +\u221e.<\/span><\/li>\n
        5. En deduire que la suite ()\u00a0est-elle convergente.<\/span><\/li>\n<\/ol>\n

          Exercice IV<\/span><\/strong><\/p>\n

            \n
          1. Sans se servir de la r\u00e8gle de l\u2019hospital<\/span>
            \na<\/strong>. Calculer la limite quand x tend vers<\/span>b<\/strong>. Calculer la limite quand x tend vers<\/span><\/li>\n
          2. Calculer les int\u00e9grales<\/span><\/span><\/li>\n
          3. D\u00e9montrer que \u2200x \u2208 [0; 1]<\/span><\/li>\n<\/ol>\n

            <\/span>Epreuves concours IUT Douala Mathematiques 2011 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2011<\/span><\/span><\/h2>\n","protected":false},"excerpt":{"rendered":"

            ...<\/p>\n","protected":false},"author":686,"featured_media":38314,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[1701],"tags":[1712,1856,1706],"class_list":["post-6785","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-epreuves","tag-epreuve-de-concours-dentree-aux-grandes-ecoles-cameroun","tag-epreuves-de-concours-de-liut-de-douala","tag-mathematiques"],"_links":{"self":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6785","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/users\/686"}],"replies":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/comments?post=6785"}],"version-history":[{"count":2,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6785\/revisions"}],"predecessor-version":[{"id":70247,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6785\/revisions\/70247"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media\/38314"}],"wp:attachment":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media?parent=6785"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=6785"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=6785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}