lim((x＋2a）/（x-a）)^(x/3)=8,x→∞求a 答案是limx→∞[(x+2a
lim((x＋2a）/（x-a）)^(x/3)=8,x→∞求a
答案是limx→∞[(x+2a)/(x-a)]^(x/3)
=limx→∞[1+ 3a/(x-a)]^(x/3)
=limx→∞[1+ 3a/(x-a)]^ [(x-a)/3a *ax/(x-a)]
=8,
顯然x趨于∞時(shí),
[1+ 3a/(x-a)]^ [(x-a)/3a]趨于e,
而ax/(x-a)趨于a,
所以
e^a=8,
于是a=ln8
但有一個(gè)問題啊,為什么求極限時(shí)底數(shù)和指數(shù)同時(shí)求極限,有l(wèi)ima^b=lima^limb嗎?怎么理解啊,