in(5x^3+x)/in(x^7+4x^2+1)求极限

题目

in(5x^3+x)/in(x^7+4x^2+1)求极限
X趋近于无穷

答案

lim(x->∞) ln(5x^3+x)/ln(x^7+4x^2+1) (∞/∞)
=lim(x->∞) (x^7+4x^2+1)(15x^2+1)/[(5x^3+x)(7x^6+8x)]
=lim(x->∞) (1+4/x^5+1/x^7)(15+1/x^2)/[(5+1/x^2)(7+8/x^5)]
=15/35
=3/7