Re: [微積] 一題極限
※ 引述《hsnuyi (羊咩咩~)》之銘言：
: cos(2x) 1
: lim [---------]^(-----) = ?
: x->∞ cos(x) x^2
: 稍微觀察一下 答案似乎是1 但是無法寫出詳細過程
: 有試過用夾擠和指數化看看能不能用l'Hospital 不過似乎不行(?)
: 懇請各位幫忙解答囉~
1. x=2npi , we know the answer is 1
2. Assume f(x) → 1 , as x→+inf
then for e , there exists d_e > 0 , s.t. when x > d_e
we have │f(x) - 1│ < e
take e = 1 , we have │f(x)│-1 =< │f(x) - 1│ < 1
so │f(x)│ < 2 , implying f is bounded for all x > d_1
this is contradictory to f is not bounded
--
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