作者siriusinlove (siriusinlove)
看板trans_math
标题Re: 问一题极限证明
时间Fri Oct 20 01:09:19 2006
※ 引述《myemail (频可欣)》之铭言：
: prove that
: lim (x-拍)cos^2[1/(x-拍)]=0
: x->拍:
Let x-π = h ==> lim (x-π)cos^2[1/(x-π)]
x-π
==> lim h (cos h) ^2
h->0
since |cos h| < 1 ==> | (cos h)^2 | < 1
==> -1 < | (cos h)^2 | < 1
==> - | h | < | h (cos h)^2 | < | h |
(注: 故意把等号拿掉不然打出来很难看...
而且当h在0的附近不等於0 时 等号也可拿掉 )
前後都逼向0 so lim h (cos h) ^2 = 0
h->0
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