求x趋近于0时,(1+x)的a次方-1除以x的极限

2025-03-07 03:51:58
推荐回答(1个)
回答1:

lim(x→0)((1+x)^a-1)/x
=lim(x→0)(e^(aln(1+x))-1)/(aln(1+x))*aln(1+x)/x
=1*a (等价无穷小,而且lim(x→0)aln(1+x)=0)
=a