Question

lim(sinx/x)^x^3,x趋于0时，求极限

lim(sinx/x)^x^3,x趋于0时，求极限

Answer 1

L =lim(x->0)(sinx/x)^x^3

lnL = lim(x->0)ln(sinx/x) / (1/x^3) (0/0)
= lim(x->0)[(x/sinx)( xcosx -sinx)/x^2 ] / (-3/x^4)
= -lim(x->0)[(x^3/sinx)( xcosx -sinx) ] /3
=0
L = 1

追问

答案错了吗？答案是2

追答

lim(x->0)(sinx/x)^(x^3)
有没有错？、

如果没错
lim(x->0)(sinx/x)^(x^3) ->1
我肯定！