QCM continuité et dérivibabilité des fonctions numeriques 0 etude de fonctions, QCM, QCM analyse numérique, QCM continuité, QCM dérivabilité, QCM développement limité, QCM étude asymptotique, qcm partie entière 16 h 24 <!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd"--> <html xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en"> <head> <title>QCM continuité et dérivibabilité des fonctions numeriques </title> <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_SVG"></script> </head> <body> <!-- MathMagic Pro Win v7.7, MathML 2.0 converter, 2015.8.30 00:16 --> <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mstyle mathcolor="#000000" mathsize="10.0pt" mathvariant="normal"> <mtable> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathvariant="italic">Question</mi> <mspace width="0.33em"/> <mn mathcolor="#0000ff">1</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Soit</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mspace width="0.33em"/> <mi mathvariant="italic">une</mi> <mspace width="0.33em"/> <mi mathvariant="italic">fonction</mi> <mspace width="0.33em"/> <mi mathvariant="italic">d</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">finie</mi> <mi mathvariant="normal">,</mi> <mspace width="0.33em"/> <mi mathvariant="italic">continue</mi> <mspace width="0.33em"/> <mi mathvariant="italic">et</mi> <mspace width="0.33em"/> <mi mathvariant="italic">strictement</mi> <mspace width="0.33em"/> <mi mathvariant="italic">monotone</mi> <mspace width="0.33em"/> <mi mathvariant="italic">de</mi> <mspace width="0.33em"/> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">sur</mi> <mspace width="0.33em"/> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Alors</mi> <mspace width="0.33em"/> <mi mathvariant="italic">pour</mi> <mspace width="0.33em"/> <mi mathvariant="italic">tout</mi> <mspace width="0.33em"/> <mo mathvariant="italic">α</mo> <mo>∊</mo> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">l</mi> <mi mathvariant="normal">'</mi> <mi mathvariant="italic">equation</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <msup> <mi mathvariant="italic">x</mi> <mn mathsize="85.0%">2</mn> </msup> </mfenced> <mo>=</mo> <mo mathvariant="italic">α</mo> <mspace width="0.33em"/> <mi mathvariant="italic">admet</mi> <mspace width="0.33em"/> <mi mathvariant="normal">:</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"/> <mi mathvariant="italic">une</mi> <mspace width="0.33em"/> <mi mathvariant="italic">solution</mi> <mspace width="0.33em"/> <mi mathvariant="italic">unique</mi> <mspace width="0.33em"/> <mi mathvariant="italic">dans</mi> <mspace width="0.33em"/> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">deux</mi> <mspace width="0.33em"/> <mi mathvariant="italic">solutions</mi> <mspace width="0.33em"/> <mi mathvariant="italic">dans</mi> <mspace width="0.33em"/> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">au</mi> <mspace width="0.33em"/> <mi mathvariant="italic">moins</mi> <mspace width="0.33em"/> <mi mathvariant="italic">deux</mi> <mspace width="0.33em"/> <mi mathvariant="italic">solutions</mi> <mspace width="0.33em"/> <mi mathvariant="italic">dans</mi> <mspace width="0.33em"/> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">z</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">ros</mi> <mspace width="0.33em"/> <mi mathvariant="italic">solutions</mi> <mspace width="0.33em"/> <mi mathvariant="italic">dans</mi> <mspace width="0.33em"/> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathvariant="italic">Question</mi> <mspace width="0.33em"/> <mn mathcolor="#0000ff">2</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">On</mi> <mspace width="0.33em"/> <mi mathvariant="italic">d</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">signe</mi> <mspace width="0.33em"/> <mi mathvariant="italic">par</mi> <mspace width="0.33em"/> <mfenced close="]" open="["> <mi mathvariant="italic">x</mi> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">la</mi> <mspace width="0.33em"/> <mi mathvariant="italic">partie</mi> <mspace width="0.33em"/> <mi mathvariant="italic">ent</mi> <mo mathvariant="italic">è</mo> <mi mathvariant="italic">re</mi> <mspace width="0.33em"/> <mi mathvariant="italic">de</mi> <mspace width="0.33em"/> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">.</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <munder> <mi mathvariant="normal">lim</mi> <mrow> <mi mathsize="85.0%" mathvariant="italic">x</mi> <mo mathsize="85.0%">→</mo> <mn mathsize="85.0%">0</mn> </mrow> </munder> <mspace width="0.33em"/> <mfenced close="]" open="["> <msup> <mi mathvariant="italic">x</mi> <mn mathsize="85.0%">2</mn> </msup> </mfenced> <mo>−</mo> <msup> <mfenced close="]" open="["> <mi mathvariant="italic">x</mi> </mfenced> <mn mathsize="85.0%">2</mn> </msup> <mspace width="0.33em"/> <mi mathvariant="italic">vaut</mi> <mspace width="0.33em"/> <mi mathvariant="normal">:</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mn>0</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mn>1</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"/> <mi mathvariant="italic">n</mi> <mi mathvariant="normal">'</mi> <mi mathvariant="italic">existe</mi> <mspace width="0.33em"/> <mi mathvariant="italic">pas</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathvariant="italic">Question</mi> <mspace width="0.33em"/> <mn mathcolor="#0000ff">3</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Soit</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mspace width="0.33em"/> <mi mathvariant="normal">:</mi> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> <mspace width="0.33em"/> <mover> <mo>→</mo> <mstyle mathsize="50%"> <mspace/> </mstyle> </mover> <mo>ℝ</mo> <mi mathvariant="normal">,</mi> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mi mathvariant="italic">x</mi> <mover> <mo>→</mo> <mstyle mathsize="50%"> <mspace/> </mstyle> </mover> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">)</mi> <mo>=</mo> <mfenced close="" open="{"> <mtable> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">xE</mi> <mfenced close=")" open="("> <mstyle mathsize="14.0pt"> <mfrac> <mn>1</mn> <mi mathvariant="italic">x</mi> </mfrac> </mstyle> </mfenced> <mi mathvariant="normal">,</mi> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mi mathvariant="italic">x</mi> <mo>≠</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mn>1</mn> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mi mathvariant="normal">,</mi> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mi mathvariant="italic">x</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Quelle</mi> <mspace width="0.33em"/> <mi mathvariant="italic">affirmation</mi> <mspace width="0.33em"/> <mi mathvariant="italic">est</mi> <mspace width="0.33em"/> <mi mathvariant="italic">correcte</mi> <mspace width="0.33em"/> <mi mathvariant="normal">?</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"/> <mo>∀</mo> <mi mathvariant="italic">x</mi> <mo>∊</mo> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">)</mi> </mrow> </mfenced> <mo>=</mo> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">)</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mo>∀</mo> <mi mathvariant="italic">x</mi> <mo>∊</mo> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">)</mi> </mrow> </mfenced> <mo>=</mo> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">)</mi> <mo>+</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mo>∀</mo> <mi mathvariant="italic">x</mi> <mo>∊</mo> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">)</mi> </mrow> </mfenced> <mo>=</mo> <mi mathvariant="italic">x</mi> <mo>+</mo> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">)</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mo>∀</mo> <mi mathvariant="italic">x</mi> <mo>∊</mo> <mfenced close="]" open="["> <mrow> <mn>0</mn> <mi mathvariant="normal">,</mi> <mn>1</mn> </mrow> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mo>+</mo> <mn>1</mn> <mi mathvariant="normal">)</mi> </mrow> </mfenced> <mo>=</mo> <mi mathvariant="italic">f</mi> <mi mathvariant="normal">(</mi> <mi mathvariant="italic">x</mi> <mi mathvariant="normal">)</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathvariant="italic">Question</mi> <mspace width="0.33em"/> <mn mathcolor="#0000ff">4</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">On</mi> <mspace width="0.33em"/> <mi mathvariant="italic">pose</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mi mathvariant="italic">x</mi> </mfenced> <mo>=</mo> <mfenced close=")" open="("> <mrow> <mn>1</mn> <mo>+</mo> <mi mathvariant="italic">x</mi> </mrow> </mfenced> <mo>×</mo> <mfenced close=")" open="("> <mrow> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mi mathvariant="italic">x</mi> </mrow> </mfenced> <mo>×</mo> <mi mathvariant="normal">...</mi> <mo>×</mo> <mfenced close=")" open="("> <mrow> <mn>1</mn> <mo>+</mo> <mi mathvariant="italic">nx</mi> </mrow> </mfenced> <mi mathvariant="normal">.</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">la</mi> <mspace width="0.33em"/> <mi mathvariant="italic">valeur</mi> <mspace width="0.33em"/> <mi mathvariant="italic">de</mi> <mspace width="0.33em"/> <msup> <mi mathvariant="italic">f</mi> <mo accent="true">′</mo> </msup> <mfenced close=")" open="("> <mn>0</mn> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">est</mi> <mspace width="0.33em"/> <mi mathvariant="normal">:</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mn>1</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">n</mi> <mi mathvariant="normal">!</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"/> <mstyle mathsize="14.0pt"> <mfrac> <mrow> <mi mathvariant="italic">n</mi> <mstyle mathsize="10.0pt"> <mfenced close=")" open="("> <mrow> <mi mathsize="14.0pt" mathvariant="italic">n</mi> <mo mathsize="14.0pt">+</mo> <mn mathsize="14.0pt">1</mn> </mrow> </mfenced> </mstyle> </mrow> <mn>2</mn> </mfrac> </mstyle> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfenced> <mi mathvariant="normal">!</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathvariant="italic">Question</mi> <mspace width="0.33em"/> <mn mathcolor="#0000ff">5</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Soit</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mi mathvariant="italic">x</mi> </mfenced> <mo>=</mo> <mi mathvariant="italic">x</mi> <mo>+</mo> <mi mathvariant="normal">ln</mi> <mi mathvariant="italic">x</mi> <mspace width="0.33em"/> <mi mathvariant="italic">une</mi> <mspace width="0.33em"/> <mi mathvariant="italic">fonction</mi> <mspace width="0.33em"/> <mi mathvariant="normal">,</mi> <mi mathvariant="italic">strictement</mi> <mspace width="0.33em"/> <mi mathvariant="italic">croissante</mi> <mspace width="0.33em"/> <mi mathvariant="italic">et</mi> <mspace width="0.33em"/> <mi mathvariant="italic">bijective</mi> <mspace width="0.33em"/> <mi mathvariant="italic">de</mi> <mspace width="0.33em"/> <msubsup> <mo>ℝ</mo> <mo mathsize="85.0%">+</mo> <mo mathsize="85.0%">*</mo> </msubsup> <mspace width="0.33em"/> <mi mathvariant="italic">sur</mi> <mspace width="0.33em"/> <mo>ℝ</mo> <mspace width="0.33em"/> <mi mathvariant="normal">.</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">On</mi> <mspace width="0.33em"/> <mi mathvariant="italic">note</mi> <mspace width="0.33em"/> <mi mathvariant="italic">g</mi> <mspace width="0.33em"/> <mi mathvariant="italic">sa</mi> <mspace width="0.33em"/> <mi mathvariant="italic">fonction</mi> <mspace width="0.33em"/> <mi mathvariant="italic">r</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">ciproque</mi> <mspace width="0.33em"/> <mi mathvariant="italic">qui</mi> <mspace width="0.33em"/> <mi mathvariant="italic">est</mi> <mspace width="0.33em"/> <mi mathvariant="italic">d</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">rivable</mi> <mspace width="0.33em"/> <mi mathvariant="italic">sur</mi> <mspace width="0.33em"/> <mo>ℝ</mo> <mi mathvariant="normal">.</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Alors</mi> <mspace width="0.33em"/> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"/> <msup> <mi mathvariant="italic">g</mi> <mo accent="true">′</mo> </msup> <mfenced close=")" open="("> <mi mathvariant="italic">x</mi> </mfenced> <mo>=</mo> <mstyle mathsize="14.0pt"> <mfrac> <mrow> <mi mathvariant="italic">g</mi> <mstyle mathsize="10.0pt"> <mfenced close=")" open="("> <mi mathsize="14.0pt" mathvariant="italic">x</mi> </mfenced> </mstyle> </mrow> <mrow> <mi mathvariant="italic">g</mi> <mstyle mathsize="10.0pt"> <mfenced close=")" open="("> <mi mathsize="14.0pt" mathvariant="italic">x</mi> </mfenced> </mstyle> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mstyle> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mo>□</mo> <mspace width="0.33em"/> <msup> <mi mathvariant="italic">g</mi> <mo accent="true">′</mo> </msup> <mfenced close=")" open="("> <mi mathvariant="italic">x</mi> </mfenced> <mo>=</mo> <mstyle mathsize="14.0pt"> <mfrac> <mrow> <mi mathvariant="italic">g</mi> <mstyle mathsize="10.0pt"> <mfenced close=")" open="("> <mi mathsize="14.0pt" mathvariant="italic">x</mi> </mfenced> </mstyle> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi mathvariant="italic">g</mi> <mstyle mathsize="10.0pt"> <mfenced close=")" open="("> <mi mathsize="14.0pt" mathvariant="italic">x</mi> </mfenced> </mstyle> </mrow> </mfrac> </mstyle> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mo>□</mo> <mspace width="0.33em"/> <msup> <mi mathvariant="italic">g</mi> <mo accent="true">′</mo> </msup> <mfenced close=")" open="("> <mi mathvariant="italic">x</mi> </mfenced> <mo>=</mo> <mn>1</mn> <mo>+</mo> <msup> <mi mathvariant="italic">e</mi> <mi mathsize="85.0%" mathvariant="italic">x</mi> </msup> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mo>□</mo> <msup> <mi mathvariant="italic">g</mi> <mo accent="true">′</mo> </msup> <mfenced close=")" open="("> <mi mathvariant="italic">x</mi> </mfenced> <mo>=</mo> <mi mathvariant="normal">ln</mi> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">g</mi> <mfenced close=")" open="("> <mi mathvariant="italic">x</mi> </mfenced> </mrow> </mfenced> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathvariant="italic">Question</mi> <mspace width="0.33em"/> <mn mathcolor="#0000ff">6</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <munder> <mi mathvariant="normal">lim</mi> <mrow> <mi mathsize="85.0%" mathvariant="italic">x</mi> <mo mathsize="85.0%">→</mo> <mn mathsize="85.0%">0</mn> </mrow> </munder> <mspace width="0.33em"/> <mstyle mathsize="14.0pt"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mi mathvariant="italic">cos</mi> <mstyle mathsize="10.0pt"> <mfenced close=")" open="("> <mi mathsize="14.0pt" mathvariant="italic">x</mi> </mfenced> </mstyle> <mi mathvariant="italic">cos</mi> <mstyle mathsize="10.0pt"> <mfenced close=")" open="("> <mrow> <mn mathsize="14.0pt">2</mn> <mi mathsize="14.0pt" mathvariant="italic">x</mi> </mrow> </mfenced> </mstyle> <mi mathvariant="italic">cos</mi> <mstyle mathsize="10.0pt"> <mfenced close=")" open="("> <mrow> <mn mathsize="14.0pt">3</mn> <mi mathsize="14.0pt" mathvariant="italic">x</mi> </mrow> </mfenced> </mstyle> </mrow> <msup> <mi mathvariant="italic">x</mi> <mn mathsize="10.0pt">2</mn> </msup> </mfrac> </mstyle> <mspace width="0.33em"/> <mi mathvariant="italic">vaut</mi> <mspace width="0.33em"/> <mi mathvariant="normal">:</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"/> <mn>7</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mn>0</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mo>+</mo> <mo>∞</mo> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">n</mi> <mi mathvariant="normal">'</mi> <mi mathvariant="italic">admet</mi> <mspace width="0.33em"/> <mi mathvariant="italic">pas</mi> <mspace width="0.33em"/> <mi mathvariant="italic">de</mi> <mspace width="0.33em"/> <mi mathvariant="normal">lim</mi> <mi mathvariant="italic">ite</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathvariant="italic">Question</mi> <mspace width="0.33em"/> <mn mathcolor="#0000ff">7</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Soit</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mspace width="0.33em"/> <mi mathvariant="italic">une</mi> <mspace width="0.33em"/> <mi mathvariant="italic">fonction</mi> <mspace width="0.33em"/> <mi mathvariant="italic">polynomiale</mi> <mspace width="0.33em"/> <mi mathvariant="italic">r</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">elle</mi> <mspace width="0.33em"/> <mi mathvariant="italic">v</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">rifiant</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mrow> <mi mathvariant="italic">x</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfenced> <mo>=</mo> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mi mathvariant="italic">x</mi> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">pour</mi> <mspace width="0.33em"/> <mi mathvariant="italic">tout</mi> <mspace width="0.33em"/> <mi mathvariant="italic">r</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">el</mi> <mspace width="0.33em"/> <mi mathvariant="italic">x</mi> <mspace width="0.33em"/> <mi mathvariant="italic">et</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mn>2</mn> </mfenced> <mo>=</mo> <mn>5</mn> <mspace width="0.33em"/> <mi mathvariant="italic">alors</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mstyle mathsize="14.0pt"> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </mstyle> </mfenced> <mspace width="0.33em"/> <mi mathvariant="italic">vaut</mi> <mspace width="0.33em"/> <mi mathvariant="normal">:</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mstyle mathsize="14.0pt"> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> </mstyle> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mo>□</mo> <mspace width="0.33em"/> <mstyle mathsize="14.0pt"> <mfrac> <mrow> <mo>−</mo> <mn>13</mn> </mrow> <mn>2</mn> </mfrac> </mstyle> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mo>□</mo> <mspace width="0.33em"/> <mstyle mathsize="14.0pt"> <mfrac> <mn>13</mn> <mn>2</mn> </mfrac> </mstyle> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mo>□</mo> <mspace width="0.33em"/> <mn>5</mn> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mspace width="0.33em"/> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">Aucune</mi> <mspace width="0.33em"/> <mi mathvariant="italic">de</mi> <mspace width="0.33em"/> <mi mathvariant="italic">ces</mi> <mspace width="0.33em"/> <mi mathvariant="italic">r</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">ponses</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathvariant="italic">Question</mi> <mspace width="0.33em"/> <mn mathcolor="#0000ff">8</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Soit</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mspace width="0.33em"/> <mi mathvariant="italic">une</mi> <mspace width="0.33em"/> <mi mathvariant="italic">fonction</mi> <mspace width="0.33em"/> <mi mathvariant="italic">d</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">finie</mi> <mspace width="0.33em"/> <mi mathvariant="italic">sur</mi> <mspace width="0.33em"/> <msubsup> <mo>ℝ</mo> <mo mathsize="85.0%">+</mo> <mo mathsize="10.0pt">*</mo> </msubsup> <mspace width="0.33em"/> <mi mathvariant="italic">comme</mi> <mspace width="0.33em"/> <mi mathvariant="italic">suit</mi> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mfenced close=")" open="("> <mi mathvariant="italic">t</mi> </mfenced> <mo>=</mo> <mstyle mathsize="15.6pt"> <mrow> <msubsup> <mo>∫</mo> <mn mathsize="10.0pt">0</mn> <mn mathsize="10.0pt">1</mn> </msubsup> <mstyle mathsize="14.0pt"> <mfrac> <mi mathvariant="italic">dx</mi> <mrow> <mi mathvariant="italic">t</mi> <mo>+</mo> <mi mathvariant="italic">sin</mi> <mi mathvariant="italic">x</mi> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathvariant="italic">Quelle</mi> <mspace width="0.33em"/> <mi mathvariant="italic">affirmation</mi> <mspace width="0.33em"/> <mi mathvariant="italic">est</mi> <mspace width="0.33em"/> <mi mathvariant="italic">corr</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">cte</mi> <mspace width="0.33em"/> <mi mathvariant="normal">?</mi> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mspace/> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mspace width="0.33em"/> <mi mathvariant="italic">est</mi> <mspace width="0.33em"/> <mi mathvariant="italic">croissante</mi> <mspace width="0.33em"/> <mi mathvariant="italic">et</mi> <mspace width="0.33em"/> <mi mathvariant="italic">tend</mi> <mspace width="0.33em"/> <mi mathvariant="italic">vers</mi> <mspace width="0.33em"/> <mn>0</mn> <mspace width="0.33em"/> <mi mathvariant="italic">en</mi> <mspace width="0.33em"/> <mo>+</mo> <mo>∞</mo> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mspace width="0.33em"/> <mi mathvariant="italic">est</mi> <mspace width="0.33em"/> <mi mathvariant="italic">d</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">croissante</mi> <mspace width="0.33em"/> <mi mathvariant="italic">et</mi> <mspace width="0.33em"/> <mi mathvariant="italic">tend</mi> <mspace width="0.33em"/> <mi mathvariant="italic">vers</mi> <mspace width="0.33em"/> <mn>0</mn> <mspace width="0.33em"/> <mi mathvariant="italic">en</mi> <mspace width="0.33em"/> <mo>+</mo> <mo>∞</mo> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mspace width="0.33em"/> <mi mathvariant="italic">est</mi> <mspace width="0.33em"/> <mi mathvariant="italic">croissante</mi> <mspace width="0.33em"/> <mi mathvariant="italic">et</mi> <mspace width="0.33em"/> <mi mathvariant="italic">tend</mi> <mspace width="0.33em"/> <mi mathvariant="italic">vers</mi> <mspace width="0.33em"/> <mo>+</mo> <mo>∞</mo> <mspace width="0.33em"/> <mi mathvariant="italic">en</mi> <mspace width="0.33em"/> <mo>+</mo> <mo>∞</mo> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"/> <mi mathvariant="italic">f</mi> <mspace width="0.33em"/> <mi mathvariant="italic">est</mi> <mspace width="0.33em"/> <mi mathvariant="italic">d</mi> <mo mathvariant="italic">é</mo> <mi mathvariant="italic">croissante</mi> <mspace width="0.33em"/> <mi mathvariant="italic">et</mi> <mspace width="0.33em"/> <mi mathvariant="italic">tend</mi> <mspace width="0.33em"/> <mi mathvariant="italic">vers</mi> <mspace width="0.33em"/> <mo>−</mo> <mo>∞</mo> <mspace width="0.33em"/> <mi mathvariant="italic">en</mi> <mspace width="0.33em"/> <mo>+</mo> <mo>∞</mo> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mspace/> </mtd> </mtr> </mtable> </mstyle> <annotation encoding="MathMagic">MMF.7h^V(P00cEUKLm^h5Oh5oPoJYjDjRXJhl9JGSZaEDdmS:IFdgYfYmX4[dbiKREA8bUDfXomN00C90a:*KMW)aTYTW8?;nLk1^*3`jV[j]mWlN[BlVTd__Uj|a_?9J3VKFmMQlNo[l3iNmciUJNnG))TmN4)_Ok5JGRdoCZ`RbP])gDcV2cKCLPHmMm2c6NNWdG9RnH(N|*LmK2?FHM__TO_NYZacl^^WSj)[ZMFo)5j|5Y?UlV[jPD]M;:JSjhWeLaiU_DED575bcdKWQFD?[Zo7DE;||boCj7nU1(I6NSI^|G799Pek][WmT4GAOn|nZ^^CbcV]iE39M_G2_L4bgTIiSo5jlg*K9WF??aRWnbaV^|7aPG4l(VU]D1|Im4JW54NW=4L6eI51MfAF7^VeAfKeLE]m:AbKM]fP?SjU?SjU?SJXS`gZHk?jF:ln=Z]?3;]?3)ZC]_Z2o`L;7Ca0|Xd6J)0kII]a1jiO]PU[8lL]2LZ8*4i`N0NF(ea6N;;]|KHS1oUlT2^9P8^Xa=UlU9Ra|gSK;Y|L1Y9]3P?;8Ab6(oA;PPY(IM^Y9Nl4RX[_(Mg|8I6D;bP|i`M0B0VT8Q10P[UeI9^;Yd*BG;`gU2|S3Z1Z^g1QKPM4:XYK`Zf8*067KJPdP81aKNlMmmE6)`a=P1d`1D;0GX(=njY(J0(20A0434;47U*4ZCN*4AC^SZ(|C]a6;_60h|B7J`N0X102KIbA4ARXBPTLAR5A*Z3E*0kQGMdY_J7b7alX*P)PR6=3eh8`70i3cWOPESRDndWU3Xh8RdX[ahDnh70DF;Imd0hJCg=]d0J^h);6Y2hdPT_[86J4djcZ^V0U_PVT`^7j*^):2QXY7P`63cZ21nAkG;h(1Xl:bgZBL^0D[W`Ud`)^j77iE;J57d[8?QM?i5Xn5)nGOUQA17I1AoA;;jPX]e7=i`3NeOW01ce10bf`*A^H?l10HT0Jb`HD^7OPP8d9G3S50ahCn908*8*QfeIbRheD4R^9Rh3(He=8)(d68E]9B[JWD3hd5k:18b9T:ge:JT*R(MEMA9RfkRc3|RHM)=65Q3NP3L6=lZiND[6:B93ekR)A8W55H4P*V;nQBDB)a3D5m`J9=)WGU0oG0(612:aC8TgF2*HA41n89DZk6BSl|d8X(jEC3eEfAbC;fY0RFcIDKI8?Xdn|I=X30G]0f)nB:VGbGR*X]IMmI:o`8]4?Ob?IBmP|Go9mnNf;c(Mk:E^Ab1jQYJ29k7D4Yo)A_Ji0HD;UeKfNj?FDG_oTg)2d=Aha5^9KXTDmWlfFUSeTlF*?GOHOl*Ic(|HBMF5kekYnU3bThN7^HK;|89[1VY=WfL5?WJ(|BnDhO]RlS9(`ne;B7Z)WdGeHA2G](gXNKL8RCY)B4c3)CIS5hNnK24^dG8E9|IHD1cli55TXJ*aVS2B?0=jUi5706d^N0gPoBIj[(iRWHoXV:j10If3K=5cL2X3Ea6d0VTeL0j3Ma=5O=Aaf^YHCQogJL]QC;HOm[^E`d;FL)(fg;2M)lRg;]DkaTZUc7f;d7n;XQ[_6hIiZ)N:g;4N2U^FXgK4LAEg;D*`]AhUZ)DZkUZ=)eg;DkEZ)NRg;QA|F=OcXbQc45ooH44V`]RgJPR8lSHFI(Yab]|P7W47UB(XGHH?77nL|0DcCK1]^N|_XD(RLF7k*d1IIUHoRIFGnhO;MiFHObKA[3ec78*hL)?|hJbo8DXghdCCH]7ZB|[if:9acn*n1W;DF?emKO4n^YT^;*eSlOOK;iFPahIe7__Qd)IT^n*?(=JlioJn[bjn[lKl6lXN;oLgjick:aGj_5Z`6m3_mZ7lDdja56QOe8)^^JNjC2?3CI:d|ImgfEg|FYDCdaTTLlLIZd0aHYdTA9g^`B0*4iDDF[h]XbeblHFkC92eB:?NfK[)TcfYJZB^cQ1*f5X[Ll04gU|^JmO[kk7TcYCU6VcC;6oVk]5UWK1GY_TJkH7L7o^fjj=WP=_c[Af6Bco]*]N]MJkD3Yi5GTIPQiF|B_RKUJk:Tk=E`i2;QkAHJngfif*a|*0dKW:NK_*YTWlBOhNkMQTUnQTTI(7IM1Q^j?gBUiZl]9]a3[hXE0Ml6`AlP?[8dO`^9cheiG(Glc137NG`?OF8GjV?XH?3ZD9UJa33dNIQc)ESH*a_Q`]O7e[14^FAWPT[P9]iFd?WF|HZ6n|8jaj(NWcIT6|2|i[N3]ZECNgh=lB7Lj`9;fGYKbdDJ[T*2)YD8CIXlLHSc*]VJ_7nF3i17lokkIjJc9C|iR;4R;G7MQDaFX|G?KmIL[*cMKkUSWFDh:SKCZUeSeNmGnHi]T808Bj1eV2SHU`bUDQa]MR;VR0jZkBZfD:o5`jB_iU^C:]8eRDf12g2C6MDnoOf876446*8gUUOG;kKoV`e`U?3^;VHW5cFe(aN1MC[;XSEd[[mZW95931[YiaBmMV7CK:j^|1T6MR?YNl;77L7ccE7oYf4m06SOQEf1XLkaPNNV?jX[PK|dQdMMKFEX*e:68:17IcQejHWQf3b7UL;Q|?oX2TU[MUe1eH[l46hRN9I]j^k8h|mTiMHLfk^[0]?U3gd=e?Vm;6PoJ=:;(EGS_SIE9jY1^[f;5Z|de|V4KiL3nadF5DUFFaSJ:R[FBeYi*=VT7licH(MH_ioP]6[4KI::lk*KGaWUfX_K)T_S?0nC`W3Kncgn3b|alH?ng=Li;[3RkYBJU62UbWn11c5``N|^D0dJj|:MgC41SW]`(Pm?ZIn1Po8jgVFYLS_j_8l=mADN|;?hPKn1m9nV1L0?[jGMj6TRn;hM`JK|I*Rgni=aMGQb_3`mo]h*Q3iXccb??O8=Tl3g]ae_J^IcL^gKKLN;=T:][95jSc`djNM(E6OPfK*ZGG_GFQ?EmQWeaCg_mVflJ44;]UbW_9M[kf4MUbZ_bBgVVSn[_8h;?gMYg4GcQ];8BjBM33_SPhKb3^4mnIU3a|j2^HmnD_)TdGZSi2lJ^|)1L3of:fI5nbb?mUkjd[e;=enBM1^7|733dh1jhgi*j_eM72HWcfW68b:lnia(5CE(de=e6jgjU=0Lehke1DfAQ`fh`9=4Z;jJZb|lmfc_?)DIiQ7gEHkT[b?nkLl=Sb5mDU94i;_5obM3k*8NOb(YXoej[on[5[]:A21`H9c^dRB?cWcUmEnJlcAogJ^jCUiIm3NgEU5BkW7[M;]EESme[Bd(afN2ZdMPX`lFgD)5mYbJahVnfV[F_3dHDiE6KE]_3Ikf[b*?)D)g73]0;gcBQKOEk^)^[SCOVEIki79OA(T]:7lA[0APnBQYXZ=kB53)6bHTd2^o2JXg]XlRlSDQ_HjQi5nWWPk_N;`hG_`Oo)j)i`.mmf</annotation> </semantics> </math> </body> <br/><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio6Qlv6saHpwXGs1bwgqlvR6LEU0bG1pzgBLYVkRqFpb7lc97a55yBR1_vdytb3iXvDKc2NEWoQqzMus_Gwe8pdPRIkBDWzJlS4IX4UOJf-ljJsUWMdEWbR1rIUyI2k_mygDC1Y339LTqM/s1600/QCM+math2.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio6Qlv6saHpwXGs1bwgqlvR6LEU0bG1pzgBLYVkRqFpb7lc97a55yBR1_vdytb3iXvDKc2NEWoQqzMus_Gwe8pdPRIkBDWzJlS4IX4UOJf-ljJsUWMdEWbR1rIUyI2k_mygDC1Y339LTqM/s200/QCM+math2.JPG" /></a></div> </html> QCM continuité et dérivibabilité des fonctions numeriques QCM continuité et dérivibabilité des fonctions numeriques Question ... Lire la suite »
