lim1/(sinx)^2-(cosx)^2/x^2 x趋向于0

题目

lim1/(sinx)^2-(cosx)^2/x^2 x趋向于0

答案

x趋于0时 (cosx)^2=1
所以 为 lim 1/(sinx)^2-1/x^2=0
lim[1/sinx^2-1/x^2]
=(x^2-sinx^2)/x^2*sinx^2
=(x^2-sinx^2)/x^4;
用洛必达法则求导
=(2x-sin2x)/4x^3
=(2-2cos(2x))/12x^2
=4sin(2x)/24x
=8x/24x
=1/3