x趋向于零,xcotx的极限是什么
\u5e2e\u6211\u6c42\u4e0b\u5217\u6781\u9650:lim(x\u8d8b\u5411\u4e8e0)xcotx;\u5f97\u6709\u8fc7\u7a0b\u70b9\u51fb\u653e\u5927:
\u5206\u5b50\u5206\u6bcd\u540c\u4e58\u221a(1+X+X^2)+1
\u6613\u5f970
绛旓細缁撴灉涓1锛屽洜涓哄彲鍖涓簒cosx/sinx,鑰寈/sinx鍦▁->0鏃瓒嬩簬1锛屽垯cosx鍦▁->0鏃剁瓑浜1.鎴栬呰繍鐢ㄦ礇蹇呰揪娉曞垯姹傦紙xcosx锛'=cosx-xsinx锛岋紙sinx锛夆=cosx,灏唜=0甯﹀叆锛屽緱1
绛旓細绛旓細lim(x鈫0) xcotx =lim(x鈫0) x*cosx / sinx =lim(x鈫0) x / sinx =1
绛旓細=1
绛旓細鎵浠ユ瀬闄=x/x=1,5,鐐瑰嚮鏀惧ぇ: ,2,lim(x->0)(xcotx)=lim(x->0)(xcosx/sinx)=lim(x->0)[(x/sinx)*cosx]=lim(x->0)(x/sinx)*lim(x->0)(cosx)=1*1 (搴旂敤閲嶈鏋侀檺lim(x->0)(sinx/x)=1)=1銆,0,
绛旓細lim(x鈫0)xcotx=lim(x鈫0)xcosx/sinx =lim(x鈫0)x/sinx * lim(x鈫0)cosx =1*1 =1
绛旓細lim<x鈫0>xcotx =lim<x鈫0>xcosx/sinx 鐢ㄦ礇蹇呰揪娉曞垯 =lim<x鈫0>(cosx-xsinx)/cosx =1 鏋侀檺鎬濇兂鐨勬濈淮鍔熻兘 鏋侀檺鎬濇兂鍦ㄧ幇浠f暟瀛︿箖鑷崇墿鐞嗗绛夊绉戜腑锛屾湁鐫骞挎硾鐨勫簲鐢紝杩欐槸鐢卞畠鏈韩鍥烘湁鐨勬濈淮鍔熻兘鎵鍐冲畾鐨勩傛瀬闄愭濇兂鎻ず浜嗗彉閲忎笌甯搁噺銆佹棤闄愪笌鏈夐檺鐨勫绔嬬粺涓鍏崇郴锛屾槸鍞墿杈╄瘉娉曠殑瀵圭珛缁熶竴瑙勫緥鍦...
绛旓細瑙o細xcotx=x(cosx/sinx)=cosx(x/sinx)x鈫0鏃讹紝cosx鈫1, x/sinx鈫1xcotx=cosx(x/sinx)鈫1limx cotx(x鈫0)=1 鈥鏋侀檺鈥濇槸鏁板涓井绉垎鐨勫熀纭姒傚康锛屾煇鎸囧嚱鏁颁腑鏌愪竴涓彉閲忥紝姝ゅ彉閲忓湪鍙樺寲鐨勮繃绋嬩腑锛岄愭笎鍚戞煇涓涓‘瀹氱殑鏁板糀涓嶆柇鍦伴艰繎鑰屾案杩滀笉鑳藉閲嶅悎鍒癆锛屾鍙橀噺姘歌繙瓒嬭繎鐨鍊糀鍙仛鈥滄瀬闄愬...
绛旓細璁$畻杩囩▼濡備笅锛歩mx-0 xcotx=limx-0 x(cosx/sinx)=limx-0 (x/sinx)=limx-0 cosx=1*1=1
绛旓細(x->0) lim xcotx =(x->0) lim xcosx/sinx =(x->0) lim cosx/ lim (sinx/x)=1/1 =1
绛旓細lim(x鈫0)xcotx =lim(x鈫0) x /tanx =lim(x鈫0) x /sinx *cosx 鏄剧劧鐢遍噸瑕鏋侀檺鐭ラ亾lim(x鈫0) x /sinx=1锛岃宑os0=1 鎵浠 鍘熸瀬闄= 1 瀹為檯涓婂湪x瓒嬩簬0鐨勬椂鍊锛寈鍜宼anx鏄瓑浠锋棤绌峰皬锛屾墍浠im(x鈫0) x /tanx灏辩瓑浜 1