x→0
lim (arctanx)^ln(1-x)
=lim e^ ln (arctanx)^ln(1-x)
=e^lim ln (arctanx)^ln(1-x)
考虑
lim ln (arctanx)^ln(1-x)
=lim ln(1-x) * ln(arctanx)
根据等价无穷小:ln(1+x)~x
=lim -x*ln(arctanx)
=-lim ln(arctanx) / 1/x
该极限为∞/∞型,根据L'Hospital法则
=-lim [ln(arctanx)]' / [1/x]'
=-lim 1/(arctanx)(1+x^2) / -1/x^2
=lim x^2 / (arctanx)(1+x^2)
根据等价无穷小:arctanx~x
=lim x / (1+x^2)
=0
故,原极限=e^0=1
有不懂欢迎追问有不懂欢迎追问如果满意,请及时采纳,谢谢
猜你喜欢
- 1Not only do I feel good about helping other people中的do什么意思?为什么要用它?
- 2化简:-3ab的2次方+2a的2次方b+3a的2次方b-2ab的2次方
- 3若a+1的绝对值+b-2的平方=0,求a+b的2013次方+a的2014次方-(3ab-a)的值
- 4would you like to wait for your turn?改为祈使句
- 5一辆汽车从甲地往返于甲、乙两地,已知上坡每小时行36千米,下坡每小时行48千米,来回一次共用2.8时.求甲
- 6利用你家里的电能表测量你家里某一用电器每小时消耗的电能
- 7you musn't throw rubbish on the ground的同义句
- 8Her__ name is Mary.her___name is Brown.___is 13.she ___in Class Three,Grade One.__telephone numb
- 9什么叫物理性质?什么叫化学性质?
- 10历史博物馆展出了两千多年前的新出土的一大批文物.(改病句)