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Question Number 81428 by abdomathmax last updated on 13/Feb/20

calculate lim_(x→+∞)  x^3 ln(1+e^(−x^2 ) )

$${calculate}\:{lim}_{{x}\rightarrow+\infty} \:{x}^{\mathrm{3}} {ln}\left(\mathrm{1}+{e}^{−{x}^{\mathrm{2}} } \right) \\ $$

Answered by mind is power last updated on 13/Feb/20

ln(1+e^(−x^2 ) )∼e^(−x^2 )   x^3 ln(1+e^(−x^2 ) )→0

$${ln}\left(\mathrm{1}+{e}^{−{x}^{\mathrm{2}} } \right)\sim{e}^{−{x}^{\mathrm{2}} } \\ $$$${x}^{\mathrm{3}} {ln}\left(\mathrm{1}+{e}^{−{x}^{\mathrm{2}} } \right)\rightarrow\mathrm{0} \\ $$

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