lim（x趋向无限大）x平方分之x+1 乘以cos（ x分之1） 等于多少
lim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09\u4e58\u4ee5\uff08cos1/x\uff09\u591a\u5c11lim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09\u4e58\u4ee5\uff08cos1/x\uff09
=lim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09\u4e58\u4ee5lim(x\u8d8b\u5411\u4e8e0)\uff08cos1/x\uff09
\u7531\u4e8elim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09=0\uff0c\u662f\u65e0\u7a77\u5c0f\u91cf\uff0c
\u800c|lim(x\u8d8b\u5411\u4e8e0)\uff08cos1/x\uff09|<=1,\u662f\u6709\u754c\u91cf\uff0c
\u6839\u636e\u65e0\u7a77\u5c0f\u91cf\u4e58\u4ee5\u6709\u754c\u91cf\u7b49\u4e8e\u65e0\u7a77\u5c0f\u91cf\uff0c\u77e5
lim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09\u4e58\u4ee5\uff08cos1/x\uff09=0
\u4e8b\u5b9e\u4e0a\uff0c\u5f53x\u8d8b\u8fd1\u4e8e\u96f6\u65f6\uff0ccos\uff081/x\uff09\u548csin\uff081/x\uff09\u90fd\u662f\u5728\u533a\u95f4[-1,1]
\u4e0a\u7684\u65e0\u7a77\u8df3\u53d8\u51fd\u6570\u3002
lim[(cos x)^(1/x^2) ],
=lim[1-2sin^2(x/2)]^(1/x^2)
==lim[1-x^2/2)]^(1/x^2)
=lim[1-x^2/2)]^[(-2/x^2)*(-1/2)]
=e^(-1/2)
绛旓細鍥犱负cos锛 x鍒嗕箣1锛夋槸鏈夋瀬闄愮殑锛岃秼浜庢棤绌峰ぇ鐨勬椂鍊欎负1锛屽彲浠ョ畝鍖栦负锛坙im锛坸瓒嬪悜鏃犻檺澶э級x骞虫柟鍒涔媥+1 锛*锛坙im锛坸瓒嬪悜鏃犻檺澶э級cos锛 x鍒嗕箣1锛夛級锛屽墠闈㈡瀬闄愪负0锛屾墍浠ユ讳綋鏋侀檺涓0
绛旓細lim [x(x+2)]/x²=lim (1+2/x)=1
绛旓細lim1/x^2=0
绛旓細2x)^(1 / (x^2))= exp(ln((1 - 2x)^(1 / (x^2)))= exp(1 / (x^2)ln|1 - 2x|)x -> inf lim (ln|2x| / x^2)= 0 (鐢ㄦ礇蹇呰揪娉曞垯灏卞彲璇佸嚭)鎵浠ワ紝缁撴灉鏄痚xp(0)= 1
绛旓細璇ユ瀬闄愪笉瀛樺湪锛佹垨璇存瀬闄愪负鏃犵┓澶銆
绛旓細lim(x鈫掆垶) xsinxsin1/x^2 =lim(x鈫掆垶) (1/x)sinx[sin1/x^2]/[1/x^2]=lim(x鈫掆垶) (1/x)sinx =0
绛旓細绗簩绉嶆柟娉曟湁閿欒锛岄噸瑕佹瀬闄愮敤閿欎簡銆侺=lim(x->+鈭) x^(1/x)lnL =lim(x->+鈭) lnx/x (鈭/鈭)=lim(x->+鈭) 1/x =0 L =e^0 =1 L=lim(x->+鈭) x^(1/x)=1
绛旓細瑙ｇ瓟濡備笅锛氳繘琛屽垎瀛愭湁鐞嗗寲锛屽垎瀛愬垎姣嶅悓鏃朵箻浠 [(x^2 + x)^(1/2)+(x^2 - x)^(1/2)]锛屽垎瀛x骞虫柟椤硅娑堝幓锛屼负2x锛屽垎姣嶄负(x^2 + x)^(1/2)+(x^2 - x)^(1/2)锛屽垎瀛愬垎姣嶅悓闄や互lxl锛屽垎瀛愪负2锛屽垎姣嶄负(1 + 1/x)^(1/2)+(1 - 1/x)^(1/2)锛(x 鈫 鈭),鎵浠ュ垎姣嶄负2锛...
绛旓細绛:鍘熷紡 =lim x->鈭 (1+1/(x^2-1))^x =lim x->鈭 (1+1/(x^2-1))^((x^2-1)*(x/(x^2-1))=lim x->鈭 e^(x/(x^2-1))=lim x->鈭 e^0 =1
绛旓細鏄殑锛屽洜涓烘鏃跺洜涓烘鏃x鐨勫钩鏂瑰垎涔嬩竴鏄帴杩鏃犵┓澶鐨勩倄鐨勫钩鏂规槸鎺ヨ繎鏃犵┓澶х殑锛屽悗闈㈢殑鏄帴杩戜簬闆躲傚彧鐪媥鐨勫钩鏂 浣犲彲浠ユ妸鍓嶉潰鐨勫浘鍍忕敾鍑烘潵锛屾槸骞傚嚱鏁般傛垨鑰呯敤浠ｆ暟鐨勬柟娉曚及绠楋紝鍒嗘瘝鏃犻檺灏忥紝鍒嗗瓙鏄竴锛岀粨鏋滄棤绌峰ぇ銆
