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

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

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