说明函数f(x)在点x0处有定义、有极限、连续这3个概念有什么联系
\u8bf4\u660e\u51fd\u6570f\u5728\u70b9x\u5904\u6709\u5b9a\u4e49\uff0c\u6709\u6781\u9650\uff0c\u8fde\u7eed\u8fd9\u4e09\u4e2a\u6982\u5ff5\u6709\u4ec0\u4e48\u4e0d\u540c\uff1f\u53c8\u6709\u4ec0\u4e48\u8054\u7cfb1\u3001\u8fde\u7eed\u51fd\u6570\uff0c\u5728\u5b9a\u4e49\u57df\u5185\u7684\u6bcf\u4e00\u70b9\uff0c\u90fd\u662f\u6709\u6781\u9650\u7684\uff1b
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2\u3001\u5b9a\u4e49\u57df\u5185\u7684\u6bcf\u4e00\u70b9\uff0c\u90fd\u662f\u6709\u5b9a\u4e49\u7684\uff1b
.
3\u3001\u4f46\u662f\u6709\u5b9a\u4e49\u7684\u70b9\uff0c\u5374\u4e0d\u4e00\u5b9a\u662f\u8fde\u7eed\u7684\u70b9\uff0c
\u53ef\u80fd\u662f\u8865\u5145\u5b9a\u4e49\u7684\u70b9\uff0c\u8fd9\u4e2a\u70b9\u53ef\u80fd\u662f\u5355\u72ec\u7684\u79bb\u6563\u70b9\uff1b
.
4\u3001\u5728\u5b9a\u4e49\u57df\u5185\uff0c\u6709\u5b9a\u4e49\u3001\u6709\u6781\u9650\u3001\u8fde\u7eed\uff0c\u662f\u6d51\u7136\u4e00\u4f53\u7684\u3002
\u4e09\u8005\u540c\u65f6\u6b63\u786e\uff0c\u4e0d\u53ef\u80fd\u4e09\u7f3a\u4e00\u3001\u4e09\u7f3a\u4e8c\u3002
.
5\u3001\u5bf9\u4e8e\u95f4\u65ad\u70b9\u3001\u5947\u70b9\uff0c
A\u3001\u80af\u5b9a\u662f\u4e0d\u8fde\u7eed\u7684\uff0c\u9664\u975e\u662f\u7b2c\u4e00\u7c7b\u9636\u6bb5\u70b9\uff0c\u7136\u540e\u8865\u5145\u6210\u8fde\u7eed\u51fd\u6570\uff1b
B\u3001\u95f4\u65ad\u70b9\u5904\u3001\u5947\u70b9\u5904\uff0c\u662f\u53ef\u4ee5\u8865\u5145\u5b9a\u4e49\u7684\uff1b
C\u3001\u4f46\u662f\u8865\u5145\u5b9a\u4e49\u7684\u5730\u65b9\uff0c\u4e0d\u4e00\u5b9a\u662f\u8fde\u7eed\u7684\uff0c\u4e5f\u4e0d\u4e00\u5b9a\u662f\u6709\u6781\u9650\u7684\u3002
.
\u4ec5\u6b64\u800c\u5df2\uff01
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\u3010\u656c\u8bf7\u3011
\u656c\u8bf7\u6709\u63a8\u9009\u8ba4\u8bc1\u300a\u4e13\u4e1a\u89e3\u7b54\u300b\u6743\u9650\u7684\u8fbe\u4eba\uff0c
\u5343\u4e07\u4e0d\u8981\u5c06\u672c\u4eba\u5bf9\u8be5\u9898\u7684\u89e3\u7b54\u8ba4\u8bc1\u4e3a\u300a\u4e13\u4e1a\u89e3\u7b54\u300b\u3002
.
\u4e00\u65e6\u88ab\u8ba4\u8bc1\u4e3a\u300a\u4e13\u4e1a\u89e3\u7b54\u300b\uff0c\u6240\u6709\u7f51\u53cb\u90fd\u65e0\u6cd5\u8fdb\u884c\u8bc4\u8bba\u3001\u516c\u8bae\u3001\u7ea0\u9519\u3002
\u672c\u4eba\u975e\u5e38\u9700\u8981\u503e\u542c\u5bf9\u6211\u89e3\u7b54\u7684\u5404\u79cd\u53cd\u9988\uff0c\u5373\u4f7f\u662f\u8a00\u8f9e\u6fc0\u70c8\u7684\u3001\u6279\u8bc4\u7684\u3001
\u53cd\u9a73\u7684\u8bc4\u8bba\uff0c\u4e5f\u662f\u9700\u8981\u503e\u542c\u7684\u3002
.
\u8bf7\u4f53\u8c05\uff0c\u656c\u8bf7\u5207\u52ff\u8ba4\u8bc1\u3002\u8c22\u8c22\u4f53\u8c05\uff01\u8c22\u8c22\u7406\u89e3\uff01\u8c22\u8c22\uff01\u8c22\u8c22\uff01
\u6709\u5b9a\u4e49\u53ea\u662f\u8bf4\u51fd\u6570\u5728x=x0\u5904\u6709\u610f\u4e49\uff0cf(x0)\u6709\u503c\u3002
\u6709\u6781\u9650\uff1a\u5728\u6709\u5b9a\u4e49\u7684\u57fa\u7840\u4e0a\uff0c\u5982\u679cx\u4ece\u67d0\u4e00\u65b9\u5411\uff08\u6b63\u5411\u6216\u8d1f\u5411\uff09\u65e0\u9650\u63a5\u8fd1x0\uff0c\u6781\u9650\u5b58\u5728\uff0c\u90a3\u4e48\u51fd\u6570\u5728x=x0\u5904\u4e00\u4fa7\u6709\u6781\u9650\u3002
\u8fde\u7eed\uff1a\u5728\u6709\u6781\u9650\u7684\u57fa\u7840\u4e0a\uff0c\u5982\u679cx=x0\u5904\u4e24\u4fa7\u7684\u6781\u9650\u5b58\u5728\u4e14\u76f8\u7b49\uff0c\u90a3\u4e48\u51fd\u6570\u5728x=x0\u5904\u8fde\u7eed\u3002
f(x) =C, 有解
（2）f(x)在点x0处有极限
lim（x-->x0+）f(x)=lim(x-->x0-)f(x) =C 【左极限=右极限】
（3）f(x)在点x0处连续
f(x) =C, 有解
绛旓細濡傛灉鍑芥暟f(x)鍦ㄧ偣x0澶勬湁瀹氫箟锛屽垯limx瓒嬭繎浜巟0锛 f(x)鑲畾瀛樺湪锛涘鏋渓imx瓒嬭繎浜巟0 锛宖(x)瀛樺湪锛屽垯鍑芥暟f(x)鍦ㄧ偣x0澶勪笉涓瀹氭湁瀹氫箟銆傛墍浠ワ紝閫夋嫨B
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绛旓細涓銆佹ц川涓嶅悓 1銆佸綋x瓒嬪悜浜x0鏃讹紝f锛坸锛瓒嬪悜浜庢棤绌峰ぇ锛屾晠x=x0涓烘棤绌烽棿鏂偣銆2銆佹尟鑽￠棿鏂偣锛岄棿鏂偣澶勭殑鏋侀檺鎸崱涓嶅瓨鍦ㄧ殑闂存柇鐐癸紝灞炰簬绗簩绫婚棿鏂偣銆備簩銆佸洓绫婚棿鏂偣涓嶅悓 1銆佸乏鍙虫瀬闄愪负鏃犵┓鐨勯棿鏂偣锛屽彨鍋氭棤绌烽棿鏂偣锛屽叾涓棤绌锋槸涓涓彲浠ヨВ鍑虹殑绛旀锛岀敤鈭炶〃绀猴紝浣嗕竴鑸涓烘瀬闄愪笉瀛樺湪銆2銆佸乏鍙...
绛旓細鏈夋瀬闄愬繀椤绘弧瓒冲乏鍙虫瀬闄愮浉绛夛紝姝ゆ椂涓嶅繀瑕佹眰鍦ㄦ鐐规湁瀹氫箟锛屽鏋滄湁瀹氫箟锛鍑芥暟鍊间笉绛変簬鏋侀檺鍊间负鍙幓闂存柇鐐癸紝鑻ユ湁瀹氫箟鍑芥暟鍊肩瓑浜庢瀬闄愬煎氨涓鸿繛缁偣锛佹湜閲囩撼锛
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绛旓細鍑芥暟 y=f(x)鍦ㄧ偣x0 澶鍙锛屾湁 lim(x鈫抶0)[f(x)-f(x0)]/(x-x0) = f'(x0)锛屼簬鏄 lim(x鈫抶0)[f(x)-f(x0)]= lim(x鈫抶0){[f(x)-f(x0)]/(x-x0)}*(x-x0)= f'(x0)*0 = 0锛屽嵆 f 鍦ㄧ偣x0澶勮繛缁傚叾閫嗕笉鐪熴備緥濡鍑芥暟f(x) = |x|鍦▁ = 0鐐澶勮繛缁絾...
绛旓細杩欎釜缁撹鍙互鍒╃敤杩炵画鎬х殑瀹氫箟鏉ヨ瘉鏄庛傚湪姝ｅ紡璇佹槑涔嬪墠锛屾垜浠厛澶嶄範涓涓嬪嚱鏁板湪鏌愮偣澶勮繛缁殑瀹氫箟銆鍑芥暟f(x)鍦ㄧ偣x0澶杩炵画锛岄渶瑕佹弧瓒充互涓嬩笁涓潯浠讹細1. f(x0)瀛樺湪锛堝嵆鍑芥暟鍦▁0澶勬湁瀹氫箟锛夛紱2. lim{x鈫抶0}f(x)瀛樺湪锛堝嵆宸﹀彸鏋侀檺鍜岀浉绛夛級锛3. lim{x鈫抶0}f(x)=f(x0)銆傜涓変釜鏉′欢璇存槑浜嗗綋x...
绛旓細姝ゆ椂锛岃嫢锛歭imf(x)/x(x瓒嬪悜浜庨浂鏃)瀛樺湪锛屽繀鏈夛細f(0)=0銆傛晠锛(x瓒嬪悜浜庨浂鏃) lim{[f(x)-f(0)]/(x-0)}=lim{f(x)/x}銆傚嵆鐭ワ細f(x)鍦▁=0澶勫彲瀵笺傜浉鍏充俊鎭細鏍规嵁鍙涓庤繛缁殑鍏崇郴瀹氱悊锛氬嚱鏁癴(x)鍦ㄧ偣x0澶勫彲瀵硷紝鍒檉(x)鍦ㄧ偣x0澶勮繛缁紝浣嗛嗗懡棰樹笉鎴愮珛銆傗鍑芥暟f(x)鍦ㄧ偣x0澶勬湁...
