Show that lim_(t->inf) (1+x/t)^t = e^x and hence show
lim_(n->inf) (1+x/n)^n = e^x.
exponential
2008-03-13 4:46 pm
回答 (1)
2008-03-13 5:27 pm
✔ 最佳答案
question is not clear, since you have not state the definition of t and n.BTW, the proof of the first part is:
e = lim_(t->inf) (1+1/t)^t
lim_(t->inf) (1+x/t)^t
= lim_(t/x->inf) ((1+x/t)^t/x )x
let y=t/x
= lim_(y->inf) ((1+1/y)^y )x
= e^x
收錄日期: 2021-04-15 01:25:12
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