Re: [極限]
※ 引述《Qmmm (Q蛆蛆)》之銘言：
: (1)極限存在時，問r應為多少
: (2)極限值=?
3 5 7
x 2x 17x
tanx = x + --- + ----- + ------ + ...
3 15 315
3 5 7
(sinx) 2(sinx) 17(sinx)
tan(sinx) = sinx + ------ + --------- + ------------- + ....
3 15 315
3 5 7 3 5 7
x x x 1 x x x 3
= (x - --- + --- - --- + ... ) + -- (x - --- + --- - --- + ... )
3! 5! 7! 3 3! 5! 7!
2 5 17 7
+ --- (懶得打 囧) + --- (囧...) + ......
15 315
1 3 1 5 3 7
= x + --- x - --- x - --- x + ....
6 40 560
3 5 7
tanx tanx tanx
而 sin(tanx) = tanx - ---- + ---- - ----
3! 5! 7!
= .....
1 3 1 5 79 7
= x + --- x - --- x - --- x + ....
6 40 840
=>
3 79 7
- --- + --- x + ...........
560 840
lim --------------------------------
x→0 r
x
故 r 為 7
3 79
極限值等於 - --- + ---
560 840
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※ 編輯: yuyumagic424 來自: 140.112.243.42 (08/27 01:01)
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