几道微积分1 lim xcot2xx-02 lim2^n sin(x/2^n) n趋向于正无穷 （x为不等于0的常数）3

1、lim(x->0) xcot2x = lim(x->0) x/tan2x
= lim(x->0)(1/2)2x/tan2x = 1/2
2、lim(x->∞)x(2^n/x) sin(x/2^n) = x
3、lim(x->0)(tanx-sinx)/x^3
= lim(x->0)[(secx)^2 - cosx]/3x^2
= lim(x->0)[2sinx/(cosx)^3 + sinx]/6x
= lim(x->0)[2(cosx)^2-6(sinx)^2/(cosx)^4 + cosx]/6
= (2 + 1)/6 = 1/2
=