求lim(x趋近于1)(x的根号m次方-1)/(x-1)
问题描述:
求lim(x趋近于1)(x的根号m次方-1)/(x-1)
答
x的根号m次方指的是x的1/m次幂吧
x->1时x^(1/m)-1
=[1+(x-1)]^(1/m)-1等价于(x-1)/m
lim(x趋近于1)(x的根号m次方-1)/(x-1)
=lim(x趋近于1)(x-1)/m(x-1)=1/m
仔细理解等价无穷小吧.这对极限计算很得要