L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer les limites suivantes.
- \( \lim{x\rightarrow +\infty} \dfrac{-2 x^{3} +\dfrac{78}{5} x^{4} +\dfrac{27}{4}+5 x^{2} +9 x }{8 x^{4} +2 x^{3} +8+2 x^{2} + x } =\)
- \( \lim{x\rightarrow +\infty} \dfrac{-3 x +4-2 x^{2} }{2 x^{4} +\dfrac{23}{2}+5 x^{2} -6 x -2 x^{3} } =\)
- \( \lim{x\rightarrow -\infty} \dfrac{-4}{-9-4 x^{3} +8 x^{2} } =\)
- \( \lim{x\rightarrow +\infty} 2 x +1-5 x^{2} -6 x^{4} +\dfrac{17}{9} x^{3} =\)
- \( \lim{x\rightarrow +\infty} \dfrac{ x^{2} +8 x +5}{7 x +5} =\)
- \( \lim{x\rightarrow +\infty} \dfrac{-6-7 x^{3} +\dfrac{73}{5} x^{4} -6 x -8 x^{2} }{-6 x -4-8 x^{3} -9 x^{4} } =\)
- \( \lim{x\rightarrow -\infty} \dfrac{5 x^{2} -\dfrac{56}{3} x -\dfrac{1}{8}}{9 x^{3} +\dfrac{31}{8} x^{2} -5 x -2} =\)
- \( \lim{x\rightarrow +\infty} \dfrac{-8 x^{3} +\dfrac{11}{2} x -2+\dfrac{55}{9} x^{4} +3 x^{2} }{-6 x^{3} +5 x } =\)
- \( \lim{x\rightarrow +\infty} \dfrac{\dfrac{37}{8} x +7-\dfrac{44}{9} x^{2} +3 x^{3} }{3 x^{2} +8 x^{4} +\dfrac{44}{9}-3 x -\dfrac{72}{5} x^{3} } =\)
- \( \lim{x\rightarrow -\infty} \dfrac{-7 x^{3} +2 x +8 x^{4} +5 x^{2} }{-4 x^{2} -\dfrac{19}{4} x +\dfrac{19}{4}} =\)
Cliquer ici pour afficher la solution
Exercice
- \( \lim{x\rightarrow +\infty} \dfrac{-2 x^{3} +\dfrac{78}{5} x^{4} +\dfrac{27}{4}+5 x^{2} +9 x }{8 x^{4} +2 x^{3} +8+2 x^{2} + x } =\dfrac{39}{20}\)
- \( \lim{x\rightarrow +\infty} \dfrac{-3 x +4-2 x^{2} }{2 x^{4} +\dfrac{23}{2}+5 x^{2} -6 x -2 x^{3} } =0\)
- \( \lim{x\rightarrow -\infty} \dfrac{-4}{-9-4 x^{3} +8 x^{2} } =0\)
- \( \lim{x\rightarrow +\infty} 2 x +1-5 x^{2} -6 x^{4} +\dfrac{17}{9} x^{3} =-\infty\)
- \( \lim{x\rightarrow +\infty} \dfrac{ x^{2} +8 x +5}{7 x +5} =+\infty\)
- \( \lim{x\rightarrow +\infty} \dfrac{-6-7 x^{3} +\dfrac{73}{5} x^{4} -6 x -8 x^{2} }{-6 x -4-8 x^{3} -9 x^{4} } =-\dfrac{73}{45}\)
- \( \lim{x\rightarrow -\infty} \dfrac{5 x^{2} -\dfrac{56}{3} x -\dfrac{1}{8}}{9 x^{3} +\dfrac{31}{8} x^{2} -5 x -2} =0\)
- \( \lim{x\rightarrow +\infty} \dfrac{-8 x^{3} +\dfrac{11}{2} x -2+\dfrac{55}{9} x^{4} +3 x^{2} }{-6 x^{3} +5 x } =-\infty\)
- \( \lim{x\rightarrow +\infty} \dfrac{\dfrac{37}{8} x +7-\dfrac{44}{9} x^{2} +3 x^{3} }{3 x^{2} +8 x^{4} +\dfrac{44}{9}-3 x -\dfrac{72}{5} x^{3} } =0\)
- \( \lim{x\rightarrow -\infty} \dfrac{-7 x^{3} +2 x +8 x^{4} +5 x^{2} }{-4 x^{2} -\dfrac{19}{4} x +\dfrac{19}{4}} =-\infty\)