求lim［ln（x＾2-x+1）/ln(x＾10+x+1)］（x趋向于正无穷）

lim［ln（x＾2-x+1）/ln(x＾10+x+1)］
=lim (2x-1 / x＾2-x+1) / (10x^9+1 / x＾10+x+1)(洛必达法则)
=lim ( x＾10+x+1)(2x-1) / ((x＾2-x+1) *(10x^9+1 ))
=2/10
=1/5

原式=lim {[(2x-1)/(x^2-x+1)]/[(10x^9+1)/(x^10+x+1)]}
=lim [(2x-1)(x^10+x+1)]/[(x^2-x+1)(10x^9+1)]
=lim [(2-1/x)(1+1/x^9+1/x^10)]/[(1-1/x+1/x^2)(10+1/x^9)]
=2/10
=1/5