lim^x^2=多少
lim2^nsinx/2^n\u7684\u6781\u9650\u662f\u591a\u5c11lim [x^2/(x^2-1)]^x
=lim [(x^2-1+1)/(x^2-1)]^x
=lim [1+1/(x^2-1)]^x
=lim {[1+1/(x^2-1)]^(x^2-1) } ^ (x/(x^2-1))
\u5927\u62ec\u53f7\u91cc\u7684\u90e8\u5206\u4e3a\u7b2c\u4e8c\u4e2a\u91cd\u8981\u6781\u9650\uff0c\u7ed3\u679c\u662fe
\u5927\u62ec\u53f7\u5916\u7684\u6307\u6570\u6781\u9650\u662f0
=e^0
=1
\u770b\u6765\u4f60\u5bf9\u7b2c\u4e8c\u4e2a\u91cd\u8981\u6781\u9650\u638c\u63e1\u5f97\u4e0d\u592a\u597d\u5662\uff0c\u8fd9\u9898\u548c\u521a\u624d\u90a3\u9898\u90fd\u662f\u7b2c\u4e8c\u4e2a\u91cd\u8981\u6781\u9650\u7684\u57fa\u672c\u9898\u3002
\u4e3b\u8981\u601d\u8def\u5c31\u662f\u51d1\u6210(1+1/a)^a\u8fd9\u4e2a\u5f62\u5f0f\uff0c\u5176\u4e2da-->\u221e
如果x趋向于无穷大，则答案是无穷大。
绛旓細濡傛灉x瓒嬪悜浜0锛屽垯绛旀鏄0锛涘鏋渪瓒嬪悜浜庢棤绌峰ぇ锛屽垯绛旀鏄棤绌峰ぇ銆
绛旓細lim^x^2 褰搙瓒嬪悜鏃犵┓澶ф椂锛寈²瓒嬪悜姝ｆ棤绌
绛旓細lim(x-->2) (x^2 - 4) = lim(x-->2) (x 2)*(x-2)鍥犱负x 2鍜寈-2鍦▁-->2杩炵画锛屾墍浠im(x-->2) (x 2)*(x-2) = lim(x-->2) (x 2)* lim(x-->2) (x-2) = (2 2)*(2-2) = 0 鎵浠im(x-->2) (x^2 - 4) = 0 鍗冲綋x瓒嬭繎浜2鏃讹紝x^2鐨勬瀬闄愮瓑浜4...
绛旓細lim锛坸-->2锛夛紙x^2-4锛 = lim锛坸-->2锛夛紙x+2锛夛紙x-2锛夊洜涓簒+2鍜寈-2鍦▁-->2杩炵画銆傛墍浠ワ細lim锛坸-->2锛夛紙x+2锛夛紙x-2锛= lim锛坸-->2锛夛紙x+2锛 lim锛坸-->2锛夛紙x-2锛= 锛2+2锛夛紙2-2锛= 0 鎵浠ワ細lim锛坸-->2锛夛紙x^2 - 4锛= 0 鍗冲綋x瓒嬭繎浜2鏃讹紝x^2鐨勬瀬闄...
绛旓細鍗曡皟鏈夌晫鍑嗗垯锛氬崟璋冨鍔狅紙鍑忓皯锛夋湁涓婏紙涓嬶級鐣岀殑鏁板垪蹇呭畾鏀舵暃銆傚湪杩愮敤浠ヤ笂涓ゆ潯鍘绘眰鍑芥暟鐨勬瀬闄愭椂灏ら渶娉ㄦ剰浠ヤ笅鍏抽敭涔嬬偣銆備竴鏄厛瑕佺敤鍗曡皟鏈夌晫瀹氱悊璇佹槑鏀舵暃锛岀劧鍚庡啀姹傛瀬闄愬笺備簩鏄簲鐢ㄥす鎸ゅ畾鐞嗙殑鍏抽敭鏄壘鍒版瀬闄愬肩浉鍚岀殑鍑芥暟 锛屽苟涓旇婊¤冻鏋侀檺鏄秼浜庡悓涓鏂瑰悜 锛屼粠鑰岃瘉鏄庢垨姹傚緱鍑芥暟 鐨勬瀬闄愬笺
绛旓細鍥炵瓟锛limx鈫2(x^2)=lim鈯縳鈫0<(x+鈯縳)^2-x^2>/鈯x=lim鈯縳鈫02X+鈯縳=2x=4
绛旓細鐢ㄥ畾涔夎瘉鏄庢瀬闄愰兘鏄牸寮忕殑鍐欐硶锛屼緷鏍风敾钁姦灏辨槸锛氶檺 |x-1|<1锛屽垯 |x+1|<2+|x-1|<3銆備换鎰忕粰瀹毼>0锛屽彇 delta = min{1,蔚/3} > 0锛屽垯褰 |x-1|<delta 鏃讹紝灏辨湁 |(x^2)-1| = |x+1||x-1| < 3|x-1| <= 蔚锛屾牴鎹瀬闄愮殑瀹氫箟锛屽緱璇併
绛旓細浠诲彇蔚>0,浠0<|x-a|<|a|/2 鍗硘a|/2<|x|<3|a|/2 |x^2-a^2|=|x+a|*|x-a|<(|x|+|a|)|x-a|<5|a|/2*|x-a|<蔚 鏈墊x-a|<2蔚/5|a| 鍙鍙 未=min{|a|/2,2蔚/5|a|} 灏辨湁 |x^2-a^2|<蔚鎭掓垚绔,鏈夋瀬闄愬畾涔夋湁:limx^2=a^2(x鈫抋).
绛旓細涔熷氨鏄瘄x+2|<5 鍙互瀵逛换鎰忕殑蔚>0锛屽嵆未=min{蔚/5,1} 褰0<|x-2|<未 |x²-2²|=|x+2||x-2|<5|x-2|<蔚鎴愮珛鎴愮珛 鎵浠lim(x瓒嬭繎浜2)x^2=4 鏋侀檺鍑芥暟鐨勬剰涔夛細鍦ㄥ尯闂(a-蔚锛宎+蔚)涔嬪鑷冲鍙湁N涓紙鏈夐檺涓級鐐癸紱鎵鏈夊叾浠栫殑鐐箈N+1锛寈N+2锛...锛堟棤闄愪釜锛夐兘钀藉湪...
绛旓細鎵浠lim(x-->2) (x^2 - 4) = 0 鍗冲綋x瓒嬭繎浜2鏃讹紝x^2鐨勬瀬闄愮瓑浜4 姹傛瀬闄愬熀鏈柟娉曟湁 1銆佸垎寮忎腑锛屽垎瀛愬垎姣嶅悓闄や互鏈楂樻锛屽寲鏃犵┓澶т负鏃犵┓灏忚绠楋紝鏃犵┓灏忕洿鎺ヤ互0浠ｅ叆锛2銆佹棤绌峰ぇ鏍瑰紡鍑忓幓鏃犵┓澶ф牴寮忔椂锛屽垎瀛愭湁鐞嗗寲锛3銆佽繍鐢ㄦ礇蹇呰揪娉曞垯锛屼絾鏄礇蹇呰揪娉曞垯鐨勮繍鐢ㄦ潯浠舵槸鍖栨垚鏃犵┓澶ф瘮鏃犵┓澶э紝鎴栨棤绌...
