lim(x->0)(1/(tanx)^2-1/(x)^2
问题描述：
lim(x->0)(1/(tanx)^2-1/(x)^2
答
lim(x->0) 1/(tanx)^2 - 1/(x)^2
= lim(x->0) [ 1/(sinx)^2 - 1 ]- 1/(x)^2
= -1 + lim(x->0) [x^2 - (sinx)^2]/x^2(sinx)^2
= -1 + lim(x->0) [x^2 - (sinx)^2]/x^4
= -1 + lim(x->0) [x - sinxcosx]/2x^3
= -1 + lim(x->0) [1 - (cosx)^2 + (sinx)^2 ]/6x^2
= -1 + lim(x->0) [2(sinx)^2 ]/6x^2
= -2/3