1.极限无穷大，算不算极限不存在 极限是正无穷是极限不存在的一种情况吗
\u6781\u9650\u4e3a\u00b1\u65e0\u7a77\u6781\u9650\u7b97\u5b58\u5728\u8fd8\u662f\u4e0d\u5b58\u5728?\u5206\u60c5\u51b5\uff0c\u5982\u679c\u51fd\u6570\u7684\u6781\u9650\u4e3a\u00b1\u65e0\u7a77\uff0c\u90a3\u4e48\u6781\u9650\u7b97\u4e0d\u5b58\u5728\u3002\u65e0\u7a77\u5927\u5e76\u4e0d\u662f\u6781\u9650\u7684\u5b58\u5728\uff0c\u5b83\u53ea\u662f\u8868\u660e\u5f53x\u8d8b\u5411\u4e8e\u65e0\u7a77\u6216\u67d0\u4e00\u7279\u5b9a\u503c\u65f6f(x)\u8d8b\u5411\u4e8e\u65e0\u7a77\u5927\uff0c\u800c\u6781\u9650\u5b58\u5728\u5fc5\u5b9a\u4e3a\u67d0\u4e00\u7279\u5b9a\u503cA\u3002
\u201c\u5f53n>N\u65f6\uff0c\u5747\u6709\u4e0d\u7b49\u5f0f|xn-a|<\u03b5\u6210\u7acb\u201d\u610f\u5473\u7740\uff1a\u6240\u6709\u4e0b\u6807\u5927\u4e8eN\u7684x0\u90fd\u843d\u5728(a-\u03b5\uff0ca+\u03b5)\u5185\uff1b\u800c\u5728(a-\u03b5\uff0ca+\u03b5)\u4e4b\u5916\uff0c\u6570\u5217{xn} \u4e2d\u7684\u9879\u81f3\u591a\u53ea\u6709N\u4e2a\uff08\u6709\u9650\u4e2a\uff09\u3002
\u5982\u679c\u5b58\u5728\u67d0 \u03b50>0\uff0c\u4f7f\u6570\u5217{xn} \u4e2d\u6709\u65e0\u7a77\u591a\u4e2a\u9879\u843d\u5728(a-\u03b50\uff0ca+\u03b50) \u4e4b\u5916\uff0c\u5219{xn} \u4e00\u5b9a\u4e0d\u4ee5a\u4e3a\u6781\u9650\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u8bbe{xn} \u662f\u4e00\u4e2a\u6570\u5217\uff0c\u5982\u679c\u5bf9\u4efb\u610f\u03b5>0\uff0c\u5b58\u5728N\u2208Z*\uff0c\u53ea\u8981 n \u6ee1\u8db3 n > N\uff0c\u5219\u5bf9\u4e8e\u4efb\u610f\u6b63\u6574\u6570p\uff0c\u90fd\u6709|xn+p-xn|<\u03b5\uff0c\u8fd9\u6837\u7684\u6570\u5217{xn} \u4fbf\u79f0\u4e3a\u67ef\u897f\u6570\u5217\u3002
\u8fd9\u79cd\u6e10\u8fdb\u7a33\u5b9a\u6027\u4e0e\u6536\u655b\u6027\u662f\u7b49\u4ef7\u7684\u3002\u5373\u4e3a\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u3002
\u6709\u9650\u5230\u65e0\u9650\u662f\u4ece\u91cf\u53d8\u5230\u8d28\u53d8\uff1b\u6709\u9650\u96c6\u7684\u6027\u8d28\u4e0d\u80fd\u63a8\u5e7f\u5230\u65e0\u9650\uff0c\u53cd\u4e4b\u4ea6\u7136\uff1b\u8981\u4f9d\u9760\u7406\u6027\u7684\u8bba\u8bc1\uff0c\u800c\u4e0d\u662f\u76f4\u89c2\u548c\u5e38\u8bc6\u6765\u8ba4\u8bc6\u65e0\u9650\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u6781\u9650
\u697c\u4e3b\u7684\u95ee\u9898\uff0c\u5982\u679c\u7ec6\u7ec6\u8ffd\u95ee\u4e0b\u53bb\uff0c\u4e00\u65b9\u9762\u4f1a\u5927\u6709\u611f\u89e6\uff0c
\u53e6\u4e00\u65b9\u9762\u4f1a\u6210\u4e3a\u4f17\u77e2\u4e4b\u7684\u3002
\u4e0b\u9762\u6cbf\u7740\u697c\u4e3b\u7684\u95ee\u9898\uff0c\u7a0d\u5fae\u5f15\u7533\u4e00\u4e0b\uff0c\u697c\u4e3b\u770b\u770b\u611f\u89c9\u5982\u4f55\uff1f
1\u3001\u6211\u4eec\u8bf4\uff0c\u6781\u9650\u5b58\u5728\u7684\u6761\u4ef6\u662f\uff1a\u5de6\u53f3\u79ef\u5206\u5206\u522b\u5b58\u5728\uff0c\u5e76\u4e14\u8fd8\u5f97\u76f8\u7b49\u3002
\u5426\u5219\uff0c\u6211\u4eec\u5c31\u94c1\u53e3\u795e\u65ad\uff1a\u6781\u9650\u4e0d\u5b58\u5728\u3002
\u6839\u636e\u4e0a\u9762\u7684\u8bf4\u6cd5\uff0c\u5355\u4fa7\u6781\u9650\uff0c\u6839\u672c\u4e0d\u662f\u6781\u9650\uff0c\u4e0d\u7b97\u6781\u9650\u5b58\u5728\uff01
\u6781\u9650\u5982\u679c\u5b58\u5728\uff0c\u4e00\u5b9a\u662f\u5de6\u6781\u9650\u3001\u53f3\u6781\u9650\uff0c\u5404\u81ea\u5b58\u5728\uff0c\u5e76\u4e14\u76f8\u7b49\u3002
\u90a3\u95ee\u9898\u6765\u4e86\uff1a
\u5e7f\u4e49\u79ef\u5206\u3001\u6687\u79ef\u5206\u7684\u7ed3\u679c\uff0c\u90fd\u662f\u5355\u4fa7\u6781\u9650\uff0c\u7b97\u4e0d\u7b97\u6781\u9650\u5b58\u5728\uff1f
\u6211\u4eec\u81ea\u6253\u8033\u5149\uff0c\u524d\u5028\u540e\u606d\u3001\u59cb\u4e71\u7ec8\u5f03\uff0c\u5982\u4f55\u4e0b\u53f0\uff1f
2\u3001\u6781\u9650\u7684\u7ed3\u679c\u662f\u65e0\u7a77\u5927\uff0c\u65e0\u8bba\u6b63\u8d1f\uff0c\u6211\u4eec\u90fd\u8bf4\u4e0d\u5b58\u5728\u3002
\u65e2\u7136\u4e0d\u5b58\u5728\uff0c\u4e3a\u4ec0\u4e48\u9b3c\u5b50\u7684\u4e60\u60ef\u662f\u5199 D.N.E. = Do Not Exist = \u4e0d\u5b58\u5728\u3002
\u4e3a\u5565\u6211\u4eec\u7ecf\u5e38\u5199\u6210 lim \u3001\u3001\u3001= \u221e\uff0c\u65e2\u7136\u7b49\u4e8e\u65e0\u7a77\u5927\uff0c\u4e3a\u4f55\u53c8\u8bf4\u4e0d\u5b58\u5728\uff1f
\u65e2\u7136\u4e0d\u5b58\u5728\uff0c\u4e3a\u4f55\u53c8\u7528\u7b49\u4e8e\u53f7\uff1f
\u221e \uff0c\u4e0d\u662f\u4e00\u4e2a\u786e\u5b9a\u7684\u6570\uff0c\u5728\u4e0d\u5b9a\u5f0f\u4e2d\uff0c\u4e00\u5171\u6709\u4e03\u79cd\u3002\u4e00\u65e6\u65ad\u5b9a\u7ed3\u679c\u662f\u221e\uff0c
\u6211\u4eec\u5c31\u662f\u5b83\u662f\u5b9a\u5f0f = determinable form\u3002
\u95ee\u9898\u53c8\u6765\u4e86\uff1a
\u221e \u7a76\u7adf\u662f\u5b9a\u5f0f\uff0c\u662f\u5ba2\u89c2\u5b58\u5728\uff1f\u8fd8\u662f\u4e0d\u5b9a\uff0c\u4e0d\u662f\u5ba2\u89c2\u5b58\u5728\uff1f
\u8fd8\u6709\u66f4\u7cdf\u7cd5\u7684\u95ee\u9898\u6765\u4e86\uff1a
\u65e0\u7a77\u5927\u4e0d\u662f\u5ba2\u89c2\u5b58\u5728\uff1f\u7a7a\u95f4\u6bcf\u5904\u7684\u67d0\u4e00\u7269\u7406\u91cf\u90fd\u662f\u65e0\u7a77\u5927\uff0c\u5728\u8fd9\u6837\u7684\u573a\u4e2d\uff0c
\u65e0\u7a77\u5927\u4e4b\u5dee\u6709\u6ca1\u6709\u7269\u7406\u610f\u4e49\uff1f\u6ca1\u6709\uff1f\u90a3\u7535\u78c1\u573a\u7406\u8bba\u521a\u521a\u88ab\u6539\u5199\uff1f
\u3001\u3001\u3001\u3001\u3001\u3001\u3001
\u7c7b\u4f3c\u7684\u95ee\u9898\u4fef\u62fe\u7686\u662f\uff0c\u8fd9\u91cc\u53cd\u6620\u4e86\u4e09\u4e2a\u95ee\u9898\uff1a
\u7b2c\u4e00\u3001\u7406\u8bba\u7684\u81ea\u6d3d\u95ee\u9898\uff0c\u5c24\u5176\u662f\u7ecf\u8fc7\u6c49\u8bd1\u4ee5\u540e\uff0c\u80fd\u5426\u4fdd\u6301\u539f\u6709\u7684\u81ea\u6d3d\uff1f
\u7b2c\u4e8c\u3001\u6211\u4eec\u6559\u5e08\u7684\u4e2a\u4eba\u5b66\u98ce\u3001\u4eba\u751f\u4fee\u517b\uff0c\u662f\u5426\u80fd\u79f0\u5f97\u4e0a\u662f\u7075\u9b42\u5de5\u7a0b\u5e08\uff1f
\u7b2c\u4e09\u3001\u6559\u5e08\u7684\u77e5\u8bc6\u9762\uff0c\u5c24\u5176\u662f\u6570\u5b66\u7269\u7406\u65b9\u6cd5\u8bba\uff0c\u662f\u4e0d\u662f\u591a\u5c5e\u6ee5\u7afd\u5145\u6570\uff1f
.
\u4e0d\u591a\u5199\u4e86\uff0c\u518d\u5199\u4e0b\u53bb\uff0c\u5c06\u4f1a\u6b7b\u65e0\u846c\u8eab\u4e4b\u5730\u3002
算
绛旓細鏋侀檺鏄井绉垎涓殑鍩虹姒傚康锛屽畠鎸囩殑鏄彉閲忓湪涓瀹氱殑鍙樺寲杩囩▼涓紝浠庢荤殑鏉ヨ閫愭笎绋冲畾鐨勮繖鏍涓绉嶅彉鍖栬秼鍔夸互鍙婃墍瓒嬪悜鐨勫硷紙鏋侀檺鍊硷級銆傛瀬闄愮殑姒傚康鏈缁堢敱鏌タ鍜岄瓘灏旀柉鐗规媺鏂瓑浜轰弗鏍奸槓杩般傚湪鐜颁唬鐨勬暟瀛﹀垎鏋愭暀绉戜功涓紝鍑犱箮鎵鏈夊熀鏈蹇碉紙杩炵画銆佸井鍒嗐佺Н鍒嗭級閮芥槸寤虹珛鍦ㄦ瀬闄愭蹇电殑鍩虹涔嬩笂銆傜嫮涔変笂鏋侀檺鏃犵┓澶鏄鏋侀檺...
绛旓細涓ユ牸鏉ヨ,鏃犵┓灞炰簬鏋侀檺涓瀛樺湪.浣嗘槸缁忓父鍑虹幇鏋侀檺涓衡垶鐨勬儏鍐,鎵浠ヨ鐨勬椂鍊欏氨璇存瀬闄愪负鈭,涔熸槸娌￠敊鐨.
绛旓細濡傛灉鏋侀檺涓鏃犵┓澶э紝璇存槑鏋侀檺涓瀛樺湪銆傞鍏堢嫮涔変笂鏋侀檺鏃犵┓澶鏄瀬闄愪笉瀛樺湪鐨涓绉嶆儏鍐点傚乏鍙虫瀬闄愪笉鐩哥瓑锛屼篃鏄瀬闄愪笉瀛樺湪鐨勪竴绉嶆儏鍐点傚湪姝ｈ礋鏃犵┓涔嬮棿鏉ュ洖闇囪崱鏄彟涓绉嶆瀬闄愪笉瀛樺湪鐨勬儏鍐点傚箍涔変笂鏋侀檺鏃犵┓澶ф槸鏋侀檺鍊兼敹鏁涗簬鏃犵┓锛屼絾宸﹀彸鏋侀檺涓嶇瓑銆侀渿鑽′粛鍒ゅ畾涓烘瀬闄愪笉瀛樺湪銆傚叾瀹炴棤绌峰ぇ骞朵笉鏄瀬闄愮殑瀛樺湪锛屽畠鍙槸琛ㄦ槑褰...
绛旓細鏋侀檺瓒嬪悜浜鏃犵┓澶鐨勬椂鍊欙紝杩欎釜鏋侀檺鏄笉瀛樺湪鐨勶紝杩欎釜鍑芥暟涔熸病鏈夋瀬鍊笺
绛旓細鏋侀檺鏄棤绌峰ぇ涓嶇畻鏋侀檺瀛樺湪銆傚嚱鏁扮殑鏋侀檺涓鏃犵┓锛屾瀬闄愮畻涓瀛樺湪銆傛棤绌峰ぇ骞朵笉鏄瀬闄愮殑瀛樺湪锛屽彧鏄〃鏄庡綋x瓒嬪悜浜庢棤绌锋垨鏌愪竴鐗瑰畾鍊兼椂f(x)瓒嬪悜浜鏃犵┓澶э紝鑰屾瀬闄愬瓨鍦ㄥ繀瀹氫负鏌愪竴鐗瑰畾鍊糀銆傜嫮涔変笂锛岀涓绫婚棿鏂偣锛堟瀬闄愬奸兘瀛樺湪锛夊彲鍘婚棿鏂偣锛堟瀬闄愬肩浉绛変絾璇ョ偣鏃犲畾涔夛級鍦ㄨ鐐瑰鏈鏋侀檺锛屾瀬闄鍊煎嵆涓哄湪璇ョ偣鐨勬瀬闄...
绛旓細鐒惰岋紝褰撴垜浠帰璁ㄥ箍涔夌殑鏋侀檺姒傚康鏃锛屾瀬闄愭棤绌峰ぇ骞朵笉浠呬粎灞闄愪簬鍑芥暟鍊艰秼杩戞棤绌峰ぇ銆傚畠鏇存繁灞傛鍦拌〃绀烘瀬闄愬肩殑鏀舵暃鎬ц川锛屽嵆鏃犺鍚戝摢涓渚ф帴杩戯紝鏋侀檺閮借秼鍚戜簬鏃犵┓銆傚敖绠″姝わ紝鑻ュ嚱鏁拌涓哄憟鐜板嚭宸﹀彸鏋侀檺涓绛夋垨鎸佺画鐨勯渿鑽★紝鍗充娇鏋侀檺鍊艰秼浜庢棤绌凤紝鎴戜滑渚濈劧浼氳瀹氳鐐圭殑鏋侀檺涓嶅瓨鍦ㄣ傚湪瀹為檯闂涓紝褰撴垜浠兂瑕佸垽鏂瀬闄...
绛旓細濡傛灉鍑芥暟鐨勬瀬闄愪负卤鏃犵┓锛岄偅涔鏋侀檺绠椾笉瀛樺湪銆傛棤绌峰ぇ骞朵笉鏄瀬闄愮殑瀛樺湪锛屽畠鍙槸琛ㄦ槑褰搙瓒嬪悜浜庢棤绌锋垨鏌愪竴鐗瑰畾鍊兼椂f(x)瓒嬪悜浜鏃犵┓澶э紝鑰屾瀬闄愬瓨鍦ㄥ繀瀹氫负鏌愪竴鐗瑰畾鍊糀銆備笌鏃犵┓澶у畾涔夋瘮杈冧究鍙緱鐭ユ棤绌峰ぇ骞朵笉鏄瀬闄愮殑瀛樺湪锛屽畠鍙槸琛ㄦ槑褰搙瓒嬪悜浜庢棤绌锋垨鏌愪竴鐗瑰畾鍊兼椂f(x)瓒嬪悜浜庢棤绌峰ぇ锛岃屾瀬闄愬瓨鍦ㄥ繀瀹氫负鏌愪竴...
绛旓細瀹氫箟涓嶅悓锛岃寖鍥翠笉鍚屻1銆佸畾涔変笉鍚岋細鏋侀檺涓嶅瓨鍦ㄦ寚涓嶅瓨鍦鏋侀檺鏋侀檺涓烘棤绌峰ぇ鎸囧瓨鍦ㄦ瀬闄愶紝浣嗚鏋侀檺涓烘棤绌峰ぇ銆2銆佽寖鍥翠笉鍚岋細鏋侀檺鏃犵┓澶鏋侀檺鍙互鍒ゆ柇鐨勫噯纭硷紝鏃犺鏄疄鏁帮紝杩樻槸鏃犵┓澶э紝鏋侀檺涓瀛樺湪涓嶅彲浠ュ垽鏂瀬闄愬硷紝涓嶅瓨鍦ㄨ繖涓暟鍊笺
绛旓細绛旓細1锛鏃犵┓澶э紝鍗筹細鈭烇紝琛ㄧず鐨勬槸涓绉嶈秼杩戠殑杩囩▼锛屼笉鏄竴涓‘瀹氱殑鍊硷紝瀹冩槸鏁板鍙橀噺鐨勪竴绉嶆ц川鎻忚堪锛屼笉鑳界洿鎺ヨ繍绠楋紝涔熶笉鑳借瀹氳寖鍥达紝鍥犳锛屸垶-鈭烇紝鈭灺封垶锛屸垶+鈭烇紝鈭灻封垶閮芥槸涓嶈兘纭畾鐨勶紝涔熸槸娌℃湁鎰忎箟鐨勩2锛鏋侀檺鏄篃鏄竴绉嶅彉閲忕殑鎬ц川鎻忚堪锛屼絾鏄湪鏁板涓紝鏋侀檺鏄湁鐣岀殑锛屾槸涓涓彲浠ョ‘瀹氳〃杩扮殑...
绛旓細銆傘傛嘲鍕掑叕寮忎箻娉曞ぉ涓嬬涓鍏堝啓鍒棶鍞夈傞噸瑕鏋侀檺鍗冪瘒涓寰嬪彇瀵规暟绫讳技棰樺簱銆傛暣浣撴硶绛変环鏃犵┓灏忛嗗悜鎬濈淮鍙屽悜鎬濈淮銆傛亽绛夊紡蟺=exp锛圠n蟺锛夈傛暟瀛楀笣鍥芥槸涓涓绠楀櫒wang椤点#HLWRC楂樻暟#锛氫笉瑕佽楠椾簡銆傘傘
