作业帮lim（X趋向于+∞）[X/(1+X²）]^X
来源：学生作业帮助网 编辑：作业帮 时间：2024/07/28 14:03:19
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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