当x趋于0时，tanx-sinx与sinx之间的关系？
(tanx-sinx)/[(sinx)^3]\u7684\u6781\u9650\u662f\uff1fx\u8d8b\u4e8e0\u8fd9\u9053\u9898\u6ca1\u90a3\u4e48\u590d\u6742\u3002 \u6211\u6765\u4e2a\u7b80\u5355\u89e3\u6cd5\uff1a
sinx~x\u6240\u4ee5\uff0c \uff08sinx\uff09^2~x^2, tanx= sinx/cosx
\u5c31\u6709(tanx-sinx)/[(sinx)^3]=(sinx/cosx-sinx)/[(sinx)^3]=(1/cosx-1)/[(sinx)^2]=(1-cosx)/(x^2cosx)
\u800cx\u8d8b\u4e8e0 cosx=1\u6240\u4ee5\u539f\u5f0f\u7b49\u4e8e\uff081-cosx\uff09/x^2
\u5229\u75281-cosx~1/2x^2
\u6240\u4ee5\u7ed3\u679c\u4e3a1/2
\u5f53 x\u8d8b\u4e8e0 \u65f6 \uff0c
tanx\uff5ex sinx\uff5ex \u7b49\u9636\u65e0\u7a77\u5c0f
\u6240\u4ee5 X\u8d8b\u4e8e0,tanx/sinx= 1
\u4e0d\u61c2\u8ffd\u95ee \uff0c \u5e0c\u671b\u80fd\u5e2e\u5230\u4f60\uff01\uff01
lim (tanx-sinx)/sinx
=lim tanx(1-cosx)/x
=lim x(x方/2)/x
=0
所以
tanx-sinx是sinx的高阶无穷小。
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绛旓細鏅曞晩 閮借浜嗘槸x瓒嬩簬0鑰屼笉鏄瓑浜0 浣犵煡閬撹繖涓瀬闄愬悧 浣犵煡閬撴棤鐞嗘暟鐨勬瀬闄愬悧 鏅
