[微積] 兩個函數在無窮大處比大小
我記得是不是有這麼一回事：
f(x+1)/f(x) > g(x+1)/g(x) | x ---> infinity, f(x), g(x) >0 for all x
→ f(x) > g(x) | x ---> infinity
還是其實根本沒有？
那有類似的嗎？
因為我用這個證出了一個錯誤的結論..
n^(1+1/n)^k < n+1 | n ---> infinity, k<1
→ (１+1/n)^k < log(n, n+1) | n ---> infinity, k<1
→ (n+1)^k / n^k < log(a, n+1)/log(a, n) | n ---> infinity, k<1, a>1
→ n^k < log(a, n) | n ---> infinity, k<1, a>1
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