Question

1+sinX的X²/1次方求极限

Answer 1

lim<x→0>(1+sinx)^(1/x^2)
= lim<x→0>[(1+sinx)^(1/sinx)]^(sinx/x^2)
= e^lim<x→0>(sinx/x^2) = e^lim<x→0>(1/x)
e^lim<x→0->(1/x) = 0, e^lim<x→0+>(1/x) = +∞
故所求极限不存在。