Question

求解这道高数极限题！！！

求解这道高数极限题！！！求解这道题……

Answer 1

😁😁

追问

您好，我想问下，为啥不能直接把tanx,sinx之类的等价代换为X呢

追答

因为不是乘，减去负号不可以，只能用泰勒公式

追问

emmmm....泰勒公式是啥？😢

追答

就是展开来

Answer 2

lim(x→π/2)(tanx)^sin2x
=e^[lim(x→π/2)sin2xlntanx
=e^[lim(x→π/2)sin2x/(1/lntanx)]
=e^[lim(x→π/2)2cos2xtanx/sec^2x]
=e^[lim(x→π/2)2cos2xsinxcosx]
=e^[lim(x→π/2)cos2xsin2x]
=e^[lim(x→π/2)1/2sin4x]
=e^[1/2sin(4×π/2)]
=e^0
=1