lim x趋于0 1-cosx^2/x^2sinX^2

问题描述:

lim x趋于0 1-cosx^2/x^2sinX^2

(1-cosx^2)/x^2sinx^2
=[1-1-2sin^2(x^2/2)]/x^2sinx^2
=2sin^2(x^2/2)/x^2sinx^2
=(x->0)2(x^2/2)^2/x^2*x^2=1/2