當x趨近於0,求lim(1-sinx)^1/x的極限值. 非常急,要詳細步驟,麻煩大家了. 答案一定有正確啊!!

當x趨近於0,求lim(1-sinx)^1/x的極限值. 非常急,要詳細步驟,麻煩大家了. 答案一定有正確啊!!

當x趨近於0,sinx等價於x
lim(1-sinx)^1/x
=lim(1-x)^1/x
=lim(1+(-x))^-(-1/x)
=lim((1+(-x))^(-1/x))^-1
=e^-1
=1/e