{"version":3,"file":"1AN11-uTDkJMdf.js","sources":["../../src/exercices/1e/1AN11.js"],"sourcesContent":["import { combinaisonListes } from '../../lib/outils/arrayOutils'\nimport {\n  ecritureAlgebrique,\n  ecritureAlgebriqueSauf1,\n  ecritureParentheseSiNegatif,\n  reduireAxPlusB\n} from '../../lib/outils/ecritures'\nimport Exercice from '../deprecatedExercice.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nexport const titre = 'Determine a tangent equation'\n\n// Les exports suivants sont optionnels mais au moins la date de publication semble essentielle\nexport const dateDePublication = '16/12/2021' // La date de publication initiale au format 'jj/mm/aaaa' pour affichage temporaire d'un tag\nexport const dateDeModifImportante = '24/10/2021' // Une date de modification importante au format 'jj/mm/aaaa' pour affichage temporaire d'un tag\n\n/**\n * Description didactique de l'exercice\n * @author\n * Référence\n*/\nexport const uuid = '4c8c7'\nexport const ref = '1AN11'\nexport default function Equationdetangente () {\n  Exercice.call(this) // Héritage de la classe Exercice()\n  this.consigne = ''\n  this.nbQuestions = 1 // Nombre de questions par défaut\n  this.nbCols = 2 // Uniquement pour la sortie LaTeX\n  this.nbColsCorr = 2 // Uniquement pour la sortie LaTeX\n  this.tailleDiaporama = 3 // Pour les exercices chronométrés. 50 par défaut pour les exercices avec du texte\n  this.video = '' // Id YouTube ou url\n  this.sup = parseInt(this.sup)\n  this.nouvelleVersion = function () {\n    this.listeQuestions = [] // Liste de questions\n    this.listeCorrections = [] // Liste de questions corrigées\n\n    let typesDeQuestionsDisponibles = [1, 2]\n    if (this.sup === 1) {\n      typesDeQuestionsDisponibles = [1]\n    }\n    if (this.sup === 2) {\n      typesDeQuestionsDisponibles = [2]\n    }\n    const listeTypeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions) // Tous les types de questions sont posés mais l'ordre diffère à chaque 'cycle'\n\n    for (let i = 0, a, b, c, texte, texteCorr, cpt = 0; i < this.nbQuestions && cpt < 50;) { // Boucle principale où i+1 correspond au numéro de la question\n      switch (listeTypeQuestions[i]) {\n        case 2 :// Sans formule\n          a = randint(-5, 5)\n          b = randint(-5, 5)// f(a)\n          c = randint(-5, 5)// f'(a)\n          texte = 'Let $f$ be a differentiable function on $[-5, 5]$ and $\\\\mathcal{C}_f$ its representative curve.<br>'\n          texte += `We know that $f(${a})=${b}~~$ and that $~~f'(${a})=${c}$.`\n          texte += `<br>Determine an equation of the tangent $(T)$ to the curve $\\\\mathcal{C}_f$ at the point of abscissa $${a}$, `\n          texte += '<br>without using the course formula of the tangent equation. '\n\n          texteCorr = 'We know that the tangent is not a vertical line, since the function is differentiable on the interval. '\n          texteCorr += `<br>We deduce that the tangent $(T)$ at the point of abscissa $${a}$, admits a reduced equation of the form:`\n          texteCorr += '$(T): y=m x + p$. <br>'\n          texteCorr += '<br>$\\\\bullet$ Determination of $m$:'\n          texteCorr += `<br>We know that the number derived in $${a}$ is by definition, the directing coefficient of the tangent at the point of abscissa $${a}$.`\n          texteCorr += `<br>Consequently, we already have: $m=f'(${a})=${c}$.`\n          texteCorr += `<br> We deduce that $(T): y= ${c} x + p$`\n          texteCorr += '<br>$\\\\bullet$ Determination of $p$:'\n          texteCorr += `<br> For this, we use that if $f(${a})=${b}~~$, then the point $A$ with coordinates $(${a},${b})$ belongs to $\\\\mathcal{C}_f$ but also to $(T)$.`\n          texteCorr += `<br> We can write $A(${a},${b}) = \\\\mathcal{C}_f \\\\cap (T)$.`\n          texteCorr += `<br> We then replace the coordinates of $A(${a},${b})$ in the equation $(T): y= ${c} x + p$.`\n          texteCorr += `<br> $\\\\begin{aligned} \\\\phantom{\\\\iff}&A(${a},${b})\\\\in (T)\\\\\\\\`\n          texteCorr += ` \\\\iff& ${b}= ${c} \\\\times ${ecritureParentheseSiNegatif(a)} + p\\\\\\\\`\n          texteCorr += ` \\\\iff& p=${b} ${ecritureAlgebriqueSauf1(-c)} \\\\times ${ecritureParentheseSiNegatif(a)} \\\\\\\\`\n          texteCorr += ` \\\\iff& p=${b} ${ecritureAlgebriqueSauf1(-c * a)} \\\\\\\\`\n          texteCorr += ` \\\\iff& p=${b - c * a}\\\\\\\\`\n          texteCorr += '\\\\end{aligned}$'\n          texteCorr += `<br>We can conclude that: $(T): y=${reduireAxPlusB(c, b - c * a)}$.`\n          break\n        case 1 :// 'formula':\n          a = randint(-5, 5)\n          b = randint(-5, 5)// f(a)\n          c = randint(-5, 5, [1])// f'(a)\n          texte = 'Let $f$ be a differentiable function on $[-5, 5]$ and $\\\\mathcal{C}_f$ its representative curve.<br>'\n          texte += `We know that $f(${a})=${b}~~$ and that $~~f'(${a})=${c}$.`\n          texte += `<br>Determine an equation of the tangent $(T)$ to the curve $\\\\mathcal{C}_f$ at the point of abscissa $${a}$, `\n          texte += '<br>using the tangent equation course formula. '\n          texteCorr = ` $${a}\\\\in[-5, 5]$ therefore the function is differentiable in $${a}$.`\n          texteCorr += `<br> We can therefore apply the course formula which gives an equation of the tangent $(T)$ at the abscissa point $${a}$:`\n          texteCorr += '<br> $\\\\begin{aligned}'\n          texteCorr += '(T): y&=f\\'(a)(x-a)+f(a)&\\\\text{We cite the course relation.}\\\\\\\\'\n          texteCorr += `(T): y&=f'(${a})(x-${ecritureParentheseSiNegatif(a)})+f(${a})&\\\\text{We apply to the statement.}\\\\\\\\`\n          texteCorr += `(T): y&=${c}(x-${ecritureParentheseSiNegatif(a)})${ecritureAlgebrique(b)}&\\\\text{We replace the known values.}\\\\\\\\`\n          if (a < 0) { texteCorr += `(T): y&=${c}(x${ecritureAlgebrique(-a)})${ecritureAlgebrique(b)}&\\\\text{We simplify the expression.}\\\\\\\\` }\n          texteCorr += `(T): y&=${reduireAxPlusB(c, -a * c)}${ecritureAlgebrique(b)}&\\\\text{We expand.}\\\\\\\\`\n\n          texteCorr += '\\\\end{aligned}$'\n          texteCorr += `<br>We can conclude that: $(T): y=${reduireAxPlusB(c, b - c * a)}$.`\n          break\n      }\n\n      // If the question has never been asked, we save it\n      if (this.questionJamaisPosee(i, texte)) { // <- laisser le i et ajouter toutes les variables qui rendent les exercices différents (par exemple a, b, c et d)\n        this.listeQuestions.push(texte)\n        this.listeCorrections.push(texteCorr)\n        i++\n      }\n      cpt++\n    }\n    listeQuestionsToContenu(this) // On envoie l'exercice à la fonction de mise en page\n  }\n  this.besoinFormulaireNumerique = ['Order', 2, '1: with formula. 2: with demonstration. 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