lim(sinx-x*cosx)/(sinx)^3,x趋于0,求极限有如下两种方法,sinx~x等价无穷小替换算出来的答案是1/2,但是直接用洛必达法则来求的答案是1/3,为什么?

lim((x+sinx)/(x-cosx))x->无穷 求lim（x-x*cosx)/(x-sinx) 求Lim(x→0)(sinx/x)^(cosx/1-cosx) Lim,x-0,(1/sinx)*(1/x-cosx/sinx)=? 为什么lim sinx/(x-π) =lim cosx/1 1、lim(x->无穷大) e^x arctanx2、lim(x->0)sinx√1+sin(1/x)3、lim(x->无穷大)【（√x^2+x+1）-【(√x^2-x+1)】4、lim(x->无穷大)((x+{x+(x)^0.5]^0.5}^0.5)/(2x+1)^0.55、lim(x->0)(sin3x+x^2sin1/x)/((1+cosx)x)6、lim(n->无穷大)(2^n)(si lim x趋于0 (sinx+x*cosx)/x=? x→∞ lim(cosx+x)/(sinx-x) 求极限? lim√x(sinx+cosx)/x+1 x→+∞ 求极限 lim x-0 1-cosx / x-sinx 当x趋近于无穷 lim(sinx+cosx)/x 是多少 lim（sinx+cosx）/x,x趋近于无穷 求LIM(1-COSX)/X*SINX X趋近于0 lim(cosx-1)/x,x趋于0,怎么化简成-sinx? Lim(sinx/x)^1/(1-cosx) X趋近于0 x趋于0 lim sinx-tanx/x^3=lim sinx/x×(cosx-1)/(x^2×cosx)是怎么通分的?x趋于0 lim sinx-tanx/x^3=lim sinx/x×(cosx-1)/(x^2×cosx)thank you lim(x趋于0)（tanx-sinx）/[(1-cosx)x] lim((x→0) (sinx/x)^1/(1-cosx)