用洛必达法则求极限 lim ln(x-3)⼀ln(e^x-e^3) 求极限。。我怎么算都得1.但是书上答案是e^3。求指点 x→3

2025-05-10 13:56:28
推荐回答(1个)
回答1:

1是正确的。
ln(x - 3)/ln(e^x - e³)
= [1/(x - 3)]/[e^x/(e^x - e³)]
= 1/(x - 3) · (e^x - e³)/e^x
= (e^x - e³)/(xe^x - 3e^x)
= e^x/(e^x + xe^x - 3e^x)
= 1/(x - 2)
= 1/(3 - 2)
= 1