分类：教育/科学-升学入学-考研
问题：考研数学若lim[sin6x+xf(x)]/x^3=0则lim[ 
若lim [sin6x+xf(x)]/x^3=0 则lim [6+f(x)]/x^2=?
 x都趋于０　答案是３６
回答：这是数学二考研真题.
lim[6+f(x)]/x^2=lim[6+f(x)]/x^2-0
=lim[6+f(x)]/x^2-lim[sin6x+xf(x)]/x^3
=lim{[6+f(x)]/x^2-[sin6x+xf(x)]/x^3}
=lim[(6x-sin6x)/x^3](洛必达法则)
=lim[(6-6cos6x)/3x^2]
=2lim[(1-cos6x)/x^2](等价无穷小代换)
=2lim[(1/2)(6x)^2/x^2]
=6^2=36