计算极限lim(n→∞)[(n+x)⼀(n-1)]^n

2024-12-05 17:31:46
推荐回答(2个)
回答1:



x=-1 lim=1,大于-1 lim=无穷,小于-1 lim=0

回答2:

(n+x)/(n-1)=1+(x+1)/(n-1)
所以不妨设1/a=(x+1)/(n-1)
n=(x+1)a+1
所以原式=lim(a→∞)(1+1/a)^[(x+1)a+1]
=lim(a→∞)(1+1/a)^(x+1)a*(1+1/a)
=lim(a→∞)[(1+1/a)^a]^(x+1)*1
=e^(x+1)