当x趋近于0 求(1+sinx)的1/x次方的极限

问题描述:

当x趋近于0 求(1+sinx)的1/x次方的极限

lim(x→0) (1+sinx)^(1/x)
=lim(x→0) (1+sinx)^[(1/sinx)(sinx/x)]
=e^lim(x→0) (sinx/x)
=e^1
=e