题目

lim(x趋近于0)(（1/sin^2 x）-(cos^2 x)/x^2)=

提问时间：2021-01-02

答案

lim(x→0)(（1/sin^2 x）-(cos^2 x)/x^2)
=lim(x→0) ((x^2-sin^2xcos^2x)/x^2*sin^2x)
=lim(x→0)((x^2-1/4sin^2(2x))/x^4) sinx与x等价无穷小量,再用罗必塔
=lim(x→0)(2x-1/2sin4x)/4x^3
=lim(x→0)(2-2cos4x)/12x^2
=lim(x→0)(8sin4x/24x)
=lim(x→0)(32cos4x/24)
=32/24=4/3