📝 Exercices de la série▼
Exercice 1Exercice 2Exercice 3Exercice 4Exercice 5Exercice 6Exercice 7Exercice 8Exercice 9Exercice 10Exercice 11Exercice 12

Exercice 9

Calculer les limites suivantes :

  • lim⁡x→−1+2+xx+1\lim\limits_{x\to -1^+} \dfrac{2+x}{x+1}

  • lim⁡x→−1−2+xx+1\lim\limits_{x\to -1^-} \dfrac{2+x}{x+1}

  • lim⁡x→3+1−x6−2x\lim\limits_{x\to 3^+} \dfrac{1-x}{6-2x}

  • lim⁡x→3−1−x6−2x\lim\limits_{x\to 3^-} \dfrac{1-x}{6-2x}

  • lim⁡x→−1+2+xx+1\lim\limits_{x \to -1^+} \dfrac{2+x}{x+1} et lim⁡x→−1−2+xx+1\lim\limits_{x \to -1^-} \dfrac{2+x}{x+1}
x−∞−1+∞x+1−0+\begin{array}{|c|ccccccc|} \hline x & -\infty && &-1& && +\infty \\ \hline x+1 & &- &&0& &+& \\ \hline \end{array} lim⁡x→−1+2+xx+1=10+=+∞\lim\limits_{x \to -1^+} \dfrac{2+x}{x+1} = \frac{1}{0^+} = +\infty lim⁡x→−1−2+xx+1=10−=−∞\lim\limits_{x \to -1^-} \dfrac{2+x}{x+1} = \frac{1}{0^-} = -\infty
  • lim⁡x→3+1−x6−2x\lim\limits_{x \to 3^+} \dfrac{1-x}{6-2x} et lim⁡x→3−1−x6−2x\lim\limits_{x \to 3^-} \dfrac{1-x}{6-2x}
x−∞3+∞6−2x+0−\begin{array}{|c|ccccccc|} \hline x & -\infty && &3& && +\infty \\ \hline 6-2x & &+ &&0& &-& \\ \hline \end{array} lim⁡x→3+1−x6−2x=−20−=+∞\lim\limits_{x \to 3^+} \dfrac{1-x}{6-2x} = \frac{-2}{0^-} = +\infty lim⁡x→3−1−x6−2x=−20+=−∞\lim\limits_{x \to 3^-} \dfrac{1-x}{6-2x} = \frac{-2}{0^+} = -\infty