a-maths!!~

As follows~~~
As follows~~~


圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/A_Hepburn02Jul111822.jpg?t=1215771920



圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/A_Hepburn03Jul111823.jpg?t=1215771929



2008-07-15 07:12:40 補充：
或許閣下的問題有不清楚的地方，但在意見欄中集合各高手之意見，終於找出c和e的答案。
c part可往:
http://i117.photobucket.com/albums/o61/billy_hywung/Jul08/Crazylim2.jpg

2008-07-15 07:12:55 補充：
d part可往:
http://i117.photobucket.com/albums/o61/billy_hywung/Jul08/Crazylim3.jpg

2008-07-15 07:14:04 補充：
多謝各位高手指點，以上兩part的更正，特別鳴謝飛天魏國大將軍張遼。

(c) By L' Hospital rule:
http://i117.photobucket.com/albums/o61/billy_hywung/Jul08/Crazylim2.jpg

(d) 條題目本身有錯: arcsin 的 domain 係 -1 <= x <= 1, 所以個 limit 應該係 tends to zero:
http://i117.photobucket.com/albums/o61/billy_hywung/Jul08/Crazylim3.jpg

我想問
lim (x->0) (arcsinx)/x 都是 1 ?

因為我發覺如果d 的答案是 1/2 的話,那

lim(x->oo) (arcsinx)/2x
= lim (n->0) [arcsin(1/n)]/2(1/n)
= lim (n->0) n[arcsin(1/n)] / 2
= 1/2 ?????/

是= 1/2嗎?

(b)
Break (2+...+n)/n^2 into 2/n^2 + .... + n/n^2,
trivially, it tends to 0 as N tends to infinity;
However, the whole thing is independent of x,
and will not change no matter how x varies.

It should not be Amaths. Amaths doesn't require arcsin and exponential function