推荐答案不严谨
应该用
lim［ln（x＾2-x+1）/ln(x＾10+x+1)］
=lim ln[x^2(1-1/x+1/x^2)]/ln[x^10(1+1/x^9+1/x^10)]
=lim [ln( x^2)+ ln(1-1/x+1/x^2) ]/[ln(x^10)+ln(1+1/x^9+1/x^10)]
=lim [2lnx+ln(1-1/x+1/x^2)]/[10lnx+ln(1+1/x^9+1/x^10)]
上下同除lnx
=lim[2+ln(1-1/x+1/x^2)/lnx]/[10+ln(1+1/x^9+1/x^10)/lnx]
然后取极限ln(1-1/x+1/x^2)/lnx->ln1/∞=0
同理ln(1+1/x^9+1/x^10)/lnx->0
所以极限=(2+0)/(10+0)
=1/5