lim[x-->正无穷]xln(1+e^x)=正无穷 (定理或性质:两个无穷大的乘积仍是无穷大)
lim[x-->负无穷]xln(1+e^x)
=lim[x-->负无穷]ln(1+e^x)/(1/x)
=lim[x-->负无穷][e^x/(1+e^x)]/(-1/x^2)
=-lim[x-->负无穷][x^2e^x]/lim[x-->负无穷](1+e^x)
=-lim[x-->负无穷][x^2e^x]
=-lim[x-->负无穷][x^2/e^(-x)]
=-lim[x-->负无穷]2x/[-e^(-x)]
=-lim[x-->负无穷]2/[e^(-x)]
=0
追问谢谢,
追答不谢