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Tutur33
117 lines
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HTML
117 lines
5.0 KiB
HTML
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<h1 id="topic_header_text">Exercice 4.8</h1>
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<a href="Lesfonctions.html">Les fonctions</a> ›› <a href="Exercices4.html">Exercices 4</a> ››
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<p class="rvps7"><span class="rvts12">★★</span><br/><span class="rvts11">1) Ecrire une fonction qui retourne la valeur de la fonction mathématique </span><span class="rvts66">f(x)= 27x</span><span class="rvts92">3</span><span class="rvts66"> -27x</span><span class="rvts92">2</span><span class="rvts66">-18x +8</span><span class="rvts11"> :</span></p>
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<p class="rvps8"><span class="rvts37">>>></span><span class="rvts38"> </span><span class="rvts40">print</span><span class="rvts38">(f(0), f(1), f(0.5), f(0.25), f(0.375))</span><br/><span class="rvts41">8.0 -10.0 -4.375 2.234375 -1.123046875</span></p>
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<p class="rvps7"><span class="rvts49">2) On se propose de chercher les zéros de cette fonction par la </span><a class="rvts85" href="http://fr.wikipedia.org/wiki/Dichotomie">méthode de dichotomie</a><span class="rvts49">.</span><br/><span class="rvts49">Ecrire le script correspondant.</span></p>
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<p class="rvps8"><span class="rvts37">>>></span><br/><span class="rvts41">Recherche d'un zéro dans l'intervalle [a,b]</span><br/><span class="rvts41">a?</span><span class="rvts38"> 0</span><br/><span class="rvts41">b?</span><span class="rvts38"> 1</span><br/><span class="rvts41">Précision ?</span><span class="rvts38"> 1e-12</span><br/><span class="rvts41">0.5</span><br/><span class="rvts41">0.25</span><br/><span class="rvts41">0.375</span><br/><span class="rvts41">0.3125</span><br/><span class="rvts41">0.34375</span><br/><span class="rvts41">0.328125</span><br/><span class="rvts41">0.3359375</span><br/><span class="rvts41">0.33203125</span><br/><span class="rvts41">0.333984375</span><br/><span class="rvts41">0.3330078125</span><br/><span class="rvts41">0.33349609375</span><br/><span class="rvts41">0.333251953125</span><br/><span class="rvts41">...</span><br/><span class="rvts41">...</span><br/><span class="rvts41">0.333333333333</span><br/><span class="rvts37">>>></span></p>
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<p class="rvps7"><span class="rvts49">3) Chercher tous les zéros de cette fonction.</span></p>
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<p class="rvps7"><span class="rvts49">Annexe : représentation graphique de la fonction </span><span class="rvts82">f(x)= 27x</span><span class="rvts91">3</span><span class="rvts82"> -27x</span><span class="rvts91">2</span><span class="rvts82"> -18x +8</span><span class="rvts49"> (graphique réalisé avec la librairie </span><a class="rvts85" href="http://matplotlib.org/examples/pylab_examples/axes_props.html">matplotlib</a><span class="rvts49"> de Python)</span></p>
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