设f(x)在x=0的邻域内具有二阶导数,且lim(x趋于0)(1+x+f(x)⼀x)^(1⼀x)=

2025-01-02 07:47:38
推荐回答(1个)
回答1:

(1)e³=e^limln(1+x+f(x)/x)/x
极限存在,故f(0)=0,limf(x)/x=0故f'(0)=0
3=lim(x+f(x)/x)/x=lim1+f(x)/x²,故f''(0)=4
(2)=e^limln(1+f(x)/x)/x=e^limf(x)/x²=e^2