lim（X趋向于+∞）[X/(1+X²）]^X

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lim（X趋向于+∞）[X/(1+X²）]^Xlim（X趋向于+∞）[X/(1+X²）]^Xlim（X趋向于+∞）[X/(1+X²）]^X取对数后求极限.很明显,limx

lim（X趋向于+∞）[X/(1+X²）]^X
lim（X趋向于+∞）[X/(1+X²）]^X

lim（X趋向于+∞）[X/(1+X²）]^X
取对数后求极限.
很明显,lim xln[x/(1+x^2)]=(+∞)ln0=(+∞)(-∞)= -∞
所以 ,原极限=e^[ lim xln[x/(1+x^2)] ]=e^(-∞)=0

等于e的负无穷即0

答案等于e