Bonjour,
je ne rédige pas ...
1) = lim sin(x)/(1 + 1/x²) = lim sin(x) n'existe pas
2) x → +∞ ⇒ 1/x → 0+ ⇒ e^(1/x) → 1+ ⇒ ... = lim x/2 = 0
3) x - 1 → 0+ et 2/(x - 1) → +∞ donc 0+
4) (3x - 2)/∛x = (∛x)³(1 - 2/∛x)/∛x = (∛x)²(1 - 2/∛x)
donc +∞ car 2/∛x → 0
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![\lim\limits_{x \to +\infty }\ln\left(\dfrac{3x-2}{\sqrt[3]{x} } \right)](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx+%5Cto+%2B%5Cinfty+%7D%5Cln%5Cleft%28%5Cdfrac%7B3x-2%7D%7B%5Csqrt%5B3%5D%7Bx%7D+%7D+%5Cright%29 "\lim\limits_{x \to +\infty }\ln\left(\dfrac{3x-2}{\sqrt[3]{x} } \right)")
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Bonjour,
je ne rédige pas ...
1) = lim sin(x)/(1 + 1/x²) = lim sin(x) n'existe pas
2) x → +∞ ⇒ 1/x → 0+ ⇒ e^(1/x) → 1+ ⇒ ... = lim x/2 = 0
3) x - 1 → 0+ et 2/(x - 1) → +∞ donc 0+
4) (3x - 2)/∛x = (∛x)³(1 - 2/∛x)/∛x = (∛x)²(1 - 2/∛x)
donc +∞ car 2/∛x → 0