当x趋近于0时,(1-cosx)的平方是sinx的 A高阶无穷小 B同届无穷小 C低阶无穷小 D等价无穷小
\u5f53x\u8d8b\u8fd1\u4e8e0\u65f6\uff0c1-cosx^2\u4e0e(sinx)^2\u76f8\u6bd4,\u54ea\u4e00\u4e2a\u662f\u9ad8\u9636\u65e0\u7a77\u5c0f\uff0c\u600e\u4e48\u8ba1\u7b97\u7684\uff1fx->0,(1-cosx)² x^4 /4 ,sinx x\u9009 A,\u9ad8\u9636\u65e0\u7a77\u5c0f
\u7531\u7b49\u4ef7\u65e0\u7a77\u5c0f\u7684\u6027\u8d28\u53ef\u77e5\uff1a\u5f53x\u21920\u65f6\uff0c1-cosx\uff5e12x2\uff0csinx\uff5ex\uff0c\u6545\uff1alimx\u21920(1?cosx)2sinx=limx\u2192012x4x=12x3\u6545\uff081-cosx\uff092\u662fsinx\u7684\u9ad8\u9636\u65e0\u7a77\u5c0f\uff0c\u6545\u9009\u62e9\uff1aA\uff0e
x->0, (1-cosx)² ~ x^4 /4 , sinx ~ x选 A，高阶无穷小
绛旓細姹傚紡瀛(1-cosx)/tanx鐨勬瀬闄愬艰秼浜0 鎵浠1-cosx鏄痶anx鐨勯珮闃舵棤绌峰皬 瀹為檯涓婅浣忓熀鏈殑绛変环鏃犵┓灏忓叕寮忓嵆鍙 x瓒嬩簬0鐨勬椂鍊 1-cosx绛変环浜0.5x^2 鑰宼anx绛変环浜巟 浜庢槸(1-cosx)/tanx绛変环浜0.5x 鍗1-cosx褰撶劧鏄痶anx鐨勯珮闃舵棤绌峰皬
绛旓細鐩存帴姹傛瀬闄 lim x鈫0 (1-cosx)/x 鍙互鐩存帴娲涘繀杈炬硶鍒 =lim sinx/1 =0 鎴栬呯瓑浠锋棤绌峰皬1-cosx~x²/2 =lim x²/2/x =lim x/2 =0 缁撴灉閮戒负0 璇存槑1-cosx鏄痻鐨勯珮闃舵棤绌峰皬
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绛旓細褰搙瓒嬭繎浜0鏃((1-cosx)sin(1/x))/x =褰搙瓒嬭繎浜0鏃((x²/2)sin(1/x))/x =1/2lim(x->0)xsin(1/x)鍥犱负x涓烘棤绌峰皬锛岃宻in(1/x)鏄湁鐣屽嚱鏁 鏃犵┓灏忓拰鏈夌晫鍑芥暟鐨勪箻绉繕鏄棤绌峰皬銆備粠鑰 鍘熷紡=0
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绛旓細鍚岄樁鏃犵┓灏忥紝鍙傝冧笅鍥撅細
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绛旓細鎮ㄥソ锛宑osx鍦▁=0澶勫彲瀵硷紝鍙蹇呯劧杩炵画锛岃繛缁繀鐒舵湁鏋侀檺锛屾晠姝ゅ鐨勬瀬闄愬煎氨绛変簬鍑芥暟鍊硷紝鍗宠浆鍖栦负姹俢os0=1銆傛偍鐨勯噰绾虫槸鎴戜滑鐨勫姩鍔涖
绛旓細x鈫0锛cox鈫1锛e^x鈫1锛屾墍浠ュ垎瀛愬垎姣嶉兘瓒嬭繎浜0 鎵浠ュ彲浠ョ敤娲涘繀杈捐寰 瀵瑰垎瀛愬垎姣嶈鲸鍒眰瀵 鍘熸瀬闄=limx鈫0锛坰inx/-e^x锛=0/-1=0
