推 suhorng:因為x^2 sin(1/x)在0的微分並非如你所想是 61.217.33.29 04/19 22:00
→ suhorng:2x sin(1/x) - cos(1/x), x代0..... 61.217.33.29 04/19 22:02
→ harry007:請問為什麼??? 220.135.184.67 04/19 22:06
→ suhorng:如果硬要l'Hopital, 分子請用定義求微分 61.217.33.29 04/19 22:06
→ suhorng:用什麼product rule等等等的rule去求微分 61.217.33.29 04/19 22:07
→ suhorng:時 前提都是"兩個微分都存在"之類 61.217.33.29 04/19 22:07
→ suhorng:現在1/x在0的微分不存在 也就不能用那些 61.217.33.29 04/19 22:08
→ suhorng:chain rule, product rule等等等去求函數 61.217.33.29 04/19 22:08
→ harry007:這題要如何判斷需要從定義下手? 220.135.184.67 04/19 22:08
→ suhorng:在 0 的微分 甚至連他存不存在都不知道 61.217.33.29 04/19 22:08
→ suhorng:這種時候 就用定義 因為無計可施 61.217.33.29 04/19 22:08
→ harry007:這樣我了解了 , 謝謝! 220.135.184.67 04/19 22:09
推 PaulErdos:但羅必達用的不是f'(a)/g'(a) 140.112.4.183 04/19 22:12
→ PaulErdos:而是 lim x->a f(x)/g(x) 140.112.4.183 04/19 22:12
→ PaulErdos:而是 lim x->a f'(x)/g'(x) 忘了撇 更正 140.112.4.183 04/19 22:12
→ suhorng:對耶@@.... 61.217.33.29 04/19 22:15
→ suhorng:嘛我之前說用定義求微分也是錯的orz 61.217.33.29 04/19 22:19
→ suhorng:沒有說在0的值是0... 61.217.33.29 04/19 22:20
→ harry007:我又混亂了= = 正確的是?? 220.135.184.67 04/19 22:28
→ suhorng:lim x/sin(x) * cos(x) * x sin(1/x) 61.217.33.29 04/19 22:30
→ suhorng:最後一個用夾擠... 61.217.33.29 04/19 22:30
→ harry007:所以這題無法使用羅必達嗎? 220.135.184.67 04/19 22:32
→ harry007:有人知道為什麼嗎= = ? 220.135.184.67 04/19 22:48