lim(x→0) tanx-sinx/x3方
lim(x\u21920) tanx-sinx/x3\u65b9\u539f\u5f0f=lim (sin/cosx - sinx)/x³
= lim sinx(1-cosx)/(x³cosx)
\u6ce8\u610f x\u4e0esinx\u662f\u7b49\u4ef7\u65e0\u7a77\u5c0f
1-cosx \u4e0e x²/2\u662f\u7b49\u4ef7\u65e0\u7a77\u5c0f
\u6240\u4ee5
\u539f\u5f0f= lim (x * x²/2)/(x³cosx)
=lim 1/(2cosx)
=1/2
lim(x\u21920) (tanx-sinx) / x³
= lim(x\u21920) tanx (1 - cosx) / x³ \u5148\u7528\u7b49\u4ef7\u65e0\u7a77\u5c0f\u4ee3\u6362 tanx ~ x
= lim(x\u21920) (1 - cosx) / x²
= lim(x\u21920) sinx / (2x) \u6d1b\u5fc5\u8fbe\u6cd5\u5219
= 1/2
lim (x * x²/2)/(x³cosx)=lim 1/(2cosx)=1/2
扩展阅读：lim sinx ∧tanx ... asinx+bcosx ... sin π x ... sin π a ... sin 兀 a ... limx无穷arctanx ... ∑∑ij i≠j ... limarctanx x趋于0 ... lnx 1 ...
