求极限lim(x→∞)(sin1⼀x+cos1⼀x)^x

求极限lim(x→∞)(sin1/x+cos1/x)^x如图需要详细过程
2025-01-19 17:03:55
推荐回答(1个)
回答1:

y=1/x
y->0
siny ~ y
cosy ~1
lim(x-> +∞) [ sin(1/x) + cos(1/x) ]^x
=lim(y-> 0) [ siny + cosy ]^(1/y)
=lim(y-> 0) ( 1 + y )^(1/y)
=e