已知lim x→0 [sin6x+xf(x)]/x^3=0,求 lim x→0 [6+f(x)]/x^2?为什么不可以这样解 因为lim x→0 [sin6x/(6x)]=1所以,lim x→0 [sin6x+xf(x)]/x^3=lim x→0 [6x+xf(x)]/x^3=lim x→0 [6+f(x)]/x^2=0这哪里错了?
问题描述:
已知lim x→0 [sin6x+xf(x)]/x^3=0,求 lim x→0 [6+f(x)]/x^2?
为什么不可以这样解
因为lim x→0 [sin6x/(6x)]=1
所以,
lim x→0 [sin6x+xf(x)]/x^3
=lim x→0 [6x+xf(x)]/x^3
=lim x→0 [6+f(x)]/x^2
=0
这哪里错了?
答