复旦高等数学答案

?

x???x?x21?x21

⑺ 原式=xlim?0??csc2 x??sin2xxlim?0?x ?0. 1

⑻ 原式=lnxxlim?0?cscx?xlim?0??cscx?cotx ?0. ⑼ 原式?e2x?ex?xe2x?ex?x 2e2xxlim?0x(ex?1)=limx?0x 2=lim?ex?1x?02x4e2x =lim ?exx?02?3

2. ⑽ 原式=lim(1?lnx)x x?0 ?

令y?(1?lnx)x 1ln(1?lnx)?(?1 )

xlim?0?lny?limx?0? 1?limx??0x?1 x 2

?xlimx?0?1?lnx?1 xlim?0??0

?x∴原式=limy?e0 x?0 ?

?1. ⑾ 令y?(2?arctanx)x ，则

l2?lnarxcta11?2

xl???imyl?nx????1x???x?x2 ??1x2 2

xlim???arctanx?1?x2?? 2∴原式=e .

1⑿ 令y?(1?sinx)x ，则