推 math1209 :MVT. 04/18 21:38
→ eggsu :對不起，我還是不知道怎麼看ln(1+1/x)-1/(x+1)>0 04/18 21:42
推 math1209 :ln(x+1) - ln x = 1/c, x < c < x+1. 04/18 22:41
※ 引述《asdfghjk (asdfghjk)》之銘言：
: ※ 引述《PttFund (批踢踢基金)》之銘言：
: : Using (1+1/n)^n → e as n→∞ to show that
: : (1+1/x)^x → e as x→+∞, and
: : (1+1/x)^x → e as x→-∞,
: : where n in N and x in R.
: let f(x) = (1+1/x)^x
: f'(x) = (1+1/x)^x [ln(1+1/x) - 1/(x+1)] > 0, for x > 0
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
請問這個不等式是怎麼看出來的啊？
: ==> f(x) is strictly increasing
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