数列的极限怎么求，求详细过程，上课老师只讲概念，根本不会。前六题。
\u7528\u6570\u5217\u6781\u9650\u5b9a\u4e49\u8bc1\u660e\uff0c\u6c42\u9ad8\u624b\u5148\u8bf4\u660e\u51fd\u6570\u6781\u9650\u6807\u51c6\u5b9a\u4e49\uff1a\u8bbe\u51fd\u6570f(x),|x|\u5927\u4e8e\u67d0\u4e00\u6b63\u6570\u65f6\u6709\u5b9a\u4e49\uff0c\u82e5\u5b58\u5728\u5e38\u6570A\uff0c\u5bf9\u4e8e\u4efb\u610f\u03b5>0\uff0c\u603b\u5b58\u5728\u6b63\u6574\u6570X\uff0c\u4f7f\u5f97\u5f53x>X\u65f6\uff0c|f(x)-A|<\u03b5\u6210\u7acb\uff0c\u90a3\u4e48\u79f0A\u662f\u51fd\u6570f(x)\u5728\u65e0\u7a77\u5927\u5904\u7684\u6781\u9650\u3002
\u8fd9\u4e2a\u662f\u9ad8\u7b49\u6570\u5b66\u91cc\u7684\u8bc1\u660e\u3002
\u8bc1\uff1a
\u5bf9\u4e8e\u4efb\u610f\u03b5\uff0c\u8981\u8bc1\u5b58\u5728N>0\uff0c\u5f53|x|>N\u65f6\uff0c\u4e0d\u7b49\u5f0f
|1/x-0|<\u03b5
\u6210\u7acb\u3002\u56e0\u4e3a\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\u76f8\u5f53\u4e8e
|1/x|<\u03b5
\u6216
|x|>1/\u03b5
\u7531\u6b64\u53ef\u77e5\uff0c\u5982\u679c\u53d6N=1/\u03b5\uff0c\u90a3\u4e48\u5f53x>N=1/\u03b5\u65f6\uff0c\u4e0d\u7b49\u5f0f|1/x-0|<\u03b5\u6210\u7acb\uff0c\u8fd9\u5c31\u8bc1\u660e\u4e86
limx\u2192\u221e(1/x)=0
\u5f80\u8bc1\uff1a\u5bf9\u4e8e\u4efb\u610f\u5c0fe>0;\u603b\u5b58\u5728\u6b63\u6574\u6570N>0;\u4f7f\u5f97\u53ea\u8981n>N\u65f6\uff0c|(n^2+1)/(n^2-1)-1|<e.
\u8bc1\u660e\uff1a\u5bf9\u4e8e\u4efb\u610f\u5c0fe>0,\u6211\u4eec\u4ee4(n^2+1)/(n^2-1)-1<e\uff1b
\u5316\u7b80\u5f97n>\u221a(2/e-1);
\u8fd9\u91cc\u6211\u4eec\u53d6N=[\u221a(2/e-1)]+1;
\u5219\u6709\u53ea\u8981n>N\u65f6\uff0c|(n^2+1)/(n^2-1)-1|<e\u603b\u6210\u7acb\u3002
\u5373(n^2+1)/(n^2-1)\u5173\u4e8en\u8d8b\u5411\u65e0\u7a77\u5927\u7684\u6781\u9650\u4e3a1\u3002
\u8bc1\u6bd5\u3002
绛旓細瀹氱悊1:濡傛灉鏁板垪{Xn}鏀舵暃锛屽垯鍏鏋侀檺鏄敮涓鐨勩傚畾鐞2:濡傛灉鏁板垪{Xn}鏀舵暃锛屽垯鍏朵竴瀹氭槸鏈夌晫鐨勩傚嵆瀵逛簬涓鍒噉(n=1,2鈥︹)锛屾诲彲浠ユ壘鍒颁竴涓鏁癕锛屼娇|Xn|鈮銆
绛旓細鏁板垪鏋侀檺鎬庝箞姹傝繃绋嬪涓嬶細涓銆佸埄鐢ㄦ瀬闄愬洓鍒欒繍绠楁硶鍒欐眰鏋侀檺 鍑芥暟鏋侀檺鐨勫洓鍒欒繍绠楁硶鍒欙細璁炬湁鍑芥暟锛岃嫢鍦ㄨ嚜鍙橀噺f锛坸锛夛紝g锛坸锛夌殑鍚屼竴鍙樺寲杩囩▼涓紝鏈塴imf锛坸锛=A锛宭img锛坸锛=B锛屽垯lim锛籪锛坸锛壜眊锛坸锛夛冀=limf锛坸锛壜眑img锛坸锛=A卤B lim锛籪锛坸锛・g锛坸锛夛冀=limf锛坸锛・limg锛...
绛旓細瑙ｉ杩囩▼濡備笅鍥撅紙鍥犳湁涓撴湁鍏紡锛屾晠鍙兘鎴浘锛夛細
绛旓細璁＄畻杩囩▼濡備笅锛(3n+2)/(5n+1)=(3+2/n)/(5+1/n)褰搉鈫掆垶鏃讹紝2/n鈫0锛1/n鈫0 閭ｄ箞 lim(n鈫掆垶)(3+2/n)/(5+1/n)=(3+0)/(5+0)=3/5 绛変环鏃犵┓灏鐨杞寲锛 锛堝彧鑳藉湪涔橀櫎鏃跺欎娇鐢紝浣嗘槸涓嶆槸璇翠竴瀹氬湪鍔犲噺鏃跺欎笉鑳界敤 浣嗘槸鍓嶆彁鏄繀椤昏瘉鏄庢媶鍒嗗悗鏋侀檺渚濈劧瀛樺湪锛 e鐨刋娆℃柟-1 鎴栬 ...
绛旓細姹傛暟鍒鏋侀檺鐨勬楠 1.璁よ瘑鏁板垪鏋侀檺鐨勫畾涔夊強鎬ц川銆傚嵆鏈缁堟暟鍒楀彂灞曞埌绗棤闄愰」鐨勬椂鍊欙紝鏁板垪鐨勬暟鍊兼槸褰掍簬涓涓浐瀹氭暟鐨勩2.浜嗚В璇佹槑鏁板垪鏋侀檺鐨勫熀鏈柟娉曘備富瑕佹槸閫氳繃鏁板垪鐨勫瓙鏁板垪杩涜璇佹槑銆3.瀛︿範渚嬮锛岀湅棰樺共瑙ｉ棶棰樸備富瑕佺湅鏁板垪鐨勫畾涔夊拰鐩稿叧鍏充簬鏁板垪鐨勯璁 4.鍒╃敤瀹氫箟鏉ヨ瘉鏄鏁板垪鐨勬瀬闄銆傛敞鎰忥紒鍙兘鍒╃敤瀹氫箟鏉...
绛旓細鏁板垪鏋侀檺鐨姹娉曪細1銆佸鏋滀唬鍏ュ悗锛屽緱鍒颁竴涓鍏蜂綋鐨勬暟瀛楋紝灏辨槸鏋侀檺銆2銆佸鏋滀唬鍏ュ悗锛屽緱鍒扮殑鏄棤绌峰ぇ锛岀瓟妗堝氨鏄瀬闄愪笉瀛樺湪銆3銆佸鏋滀唬鍏ュ悗锛屾棤娉曠‘瀹氭槸鍏蜂綋鏁版垨鏄棤绌峰ぇ锛屽氨鏄笉瀹氬紡绫诲瀷銆4銆佽绠楁瀬闄愶紝灏辨槸璁＄畻瓒嬪娍tendency銆傚瓨鍦ㄦ潯浠讹細鍗曡皟鏈夌晫瀹氱悊 鍦ㄥ疄鏁扮郴涓紝鍗曡皟鏈夌晫鏁板垪蹇鏈夋瀬闄銆傝嚧瀵嗘у畾鐞嗭紝浠讳綍...
绛旓細+1]=4/[v(1+0)+1]=2锛涳紙6锛夈佸師寮=limn鈫掆垶(2+sin^2n)^(1/n)=limt鈫0[2+sin^2(1/t)]^t =C^0=1锛涳紙8锛夈佸師寮=lim[1+1/(n+1)]^(n+1)/[1+1/(n+1)]=e/(1+0)=e锛涳紙10锛夈佸師寮=lim[1+1/(n-4)]^(n-4)*[1+1/(n-4)]^8 =e*(1+0)^8=e銆
绛旓細绛夋瘮鏁板垪姹傛瀬闄鏂规硶锛氬綋|q|<1鏃讹紝limSn=a1/(1-q)銆傚綋|q|>=1鏃讹紝鏋侀檺涓嶅瓨鍦ㄣ傜瓑姣旀暟鍒楁槸鎸囦粠绗簩椤硅捣锛屾瘡涓椤逛笌瀹冪殑鍓嶄竴椤圭殑姣斿肩瓑浜庡悓涓涓父鏁扮殑涓绉嶆暟鍒楋紝甯哥敤G銆丳琛ㄧず銆傝繖涓父鏁板彨鍋氱瓑姣旀暟鍒楃殑鍏瘮锛屽叕姣旈氬父鐢ㄥ瓧姣峲琛ㄧず(q鈮0)锛岀瓑姣旀暟鍒梐1鈮 0銆傚叾涓瓄an}涓殑姣忎竴椤瑰潎涓嶄负0銆傛敞锛歲=...
绛旓細渚嬪锛屽垽鏂暟鍒梴xn=(n-1)/(n+1)}鐨勬瀬闄鏄惁瀛樺湪骞舵眰鍑哄叾鏋侀檺锛屽彲浠ラ噰鐢ㄤ互涓姝ラ锛氬埄鐢ㄦ蹇垫硶锛屽浠绘剰鐨勬鏁拔碉紝闇瑕佹壘鍒版鏁存暟N锛屼娇寰楀綋n>N鏃讹紝|xn-A|<蔚鎭掓垚绔嬨傛牴鎹鏁板垪鐨閫氶」鍏紡锛屽彲浠ュ緱鍒皒n=1-2/(n+1)銆傚浜庝换鎰忕殑姝ｆ暟蔚锛屽綋n>2/蔚鏃讹紝鏈墊xn-1|=2/(n+1)<蔚鎴愮珛銆傚洜姝わ紝鍙朜...
绛旓細绗竴棰橈細鍒嗗紑涓ら」锛屽垎鍒姹傛瀬闄鍐嶇浉鍔犮俷瓒嬪悜浜庢棤绌锋椂锛1/n鐨勬瀬闄涓0锛1/n^2鐨勬瀬闄愪负0銆傜粨鏋滀负0 绗簲棰橈細鍚岀涓棰橈紝鍒嗗紑涓ら」姹傝В锛岀涓椤圭殑鏋侀檺涓1鏈韩锛岀浜岄」鏋侀檺涓0銆傜粨鏋滀负1
