[微積] 請教一題積分
2 (2-x)(x+x^n)
∫ lim ---------------------- dx
0 n->∞ 1+x^n
=>同除2^n
x x^n
-------+---------
2 (2-x)( 2^n 2^n )
=∫ lim --------------------------------- dx
0 n->∞ 1 x^n
------ + -------
2^n 2^n
x
-----
2 (2-x)( 2^n )
=∫ lim ---------------------- dx
0 n->∞ 1
-----
2^n
2
=∫ (2-x) x dx =4/3
0
但 正確答案是7/6 請問我哪裡錯了呢? 謝謝。
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推
05/23 23:54, , 1F
05/23 23:54, 1F
→
05/23 23:56, , 2F
05/23 23:56, 2F
推
05/23 23:57, , 3F
05/23 23:57, 3F
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05/23 23:58, , 4F
05/23 23:58, 4F
推
05/24 00:01, , 5F
05/24 00:01, 5F
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05/24 00:02, , 6F
05/24 00:02, 6F
推
05/24 00:04, , 7F
05/24 00:04, 7F
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05/24 00:06, , 8F
05/24 00:06, 8F
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05/24 00:07, , 9F
05/24 00:07, 9F
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05/24 00:08, , 10F
05/24 00:08, 10F
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05/24 00:09, , 11F
05/24 00:09, 11F
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05/24 00:09, , 12F
05/24 00:09, 12F
推
05/24 00:13, , 13F
05/24 00:13, 13F
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05/24 00:18, , 14F
05/24 00:18, 14F
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