fx在01上连续,01上可导,f0等于0,fx导数的绝对值小于等于fx,证明fx恒等于0，x属于 设fx在【0，1]上可导 |fx|<=1,f (0)=f (...
fx\u5728[0,\u65e0\u7a77],\u8fde\u7eed\u53ef\u5fae,\u4e14fx\u5bfc\u6570\u7684\u7edd\u5bf9\u503c<fx,f0=1\u8bc1\u660e,\u5f53x>0\u65f6,fx<e\u2227x\u9898\u76ee\u6709\u95ee\u9898\u54e6
绛旓細2014-11-28 fx鍦01涓婅繛缁涓攆0=f1,璇佹槑鑷冲皯瀛樺湪涓鐐筧灞炰簬寮鍖洪棿0... 3 2015-11-30 fx鍦╗0,1]涓婅繛缁,f(1)=0,f(0)=1,璇佹槑瀛樺湪... 4 2016-01-14 璁緁x鍦╗0,a]涓婅繛缁湪(0,a)鍐呭彲瀵间笖fa=0璇佹槑瀛樺湪... 30 2017-12-01 fx鍦ㄩ浂鍒版鏃犵┓涓婂彲瀵,褰揦澶т簬闆舵椂,0灏忎簬fx鐨勫鏁板皬浜1...鏇村...
绛旓細璇佹槑锛氫护g(x)=x^2锛孏(x)=g(x)*f(x)銆傚洜涓篺(x)鍦╗0,1]涓婅繛缁鍦(0,1)鍐呭彲瀵硷紝涓攇(x)鍦╗0,1]涓婅繛缁湪(0,1)鍐呭彲瀵硷紝閭ｄ箞G(x)=g(x)*f(x)鍦╗0,1]涓婅繛缁湪(0,1)鍐呭彲瀵笺備笖G(x)'=(g(x)*f(x))'=(x^2*f(x))'=x^2f'(x)+2xf(x)鑰孏(0)=g(0)*f(0)=0...
绛旓細鈭村瓨鍦╔浣肯嗭紘锕橷锕氾紳0 鍗砐f锛囷箼X锕氾紜f锕橷锕氾紳0 f锛囷箼 X锕氾紳锕锕橷锕/X
绛旓細^浠(x)=x^3*f(x)锛屽垯g(x)鍦╗0,1]涓婅繛缁紝鍦(0,1)鍐呭彲瀵 鍥犱负g(0)=0锛実(1)=f(1)=0锛屾墍浠ユ牴鎹綏灏斿畾鐞 瀛樺湪尉鈭(0,1)锛屼娇寰梘'(尉)=0 3尉^2*f(尉)+尉^3*f'(尉)=0 3f(尉)+尉f'(尉)=0 璇佹瘯 渚嬪锛氫护g(x)=xf(x),0<=x<=1.閭ｄ箞g(0)=g(1)=0锛実'(x...
绛旓細璁惧嚱鏁癴(x)鍦ㄣ0,1銆涓婅繛缁,鍦(0,1)鍐呭彲瀵,涓攆(0)=f(1)=0,璇佹槑鍦(0,1)鍐呰嚦灏戞湁涓鐐刮,浣垮緱f(尉)+2f'(尉)=0 www8694331 | 娴忚1114 娆 闂鏈紑鏀惧洖绛 |涓炬姤 鎺ㄨ崘浜2017-12-15 10:22:22 鏈浣崇瓟妗 F=f(x)e^(x/2),F鍦ㄥ尯闂碵0,1]婧瓒崇綏灏斿畾鐞嗙殑鏉′欢.鐢辩綏灏斿畾鐞,鍦(0,1)鍐呰嚦灏戞湁...
绛旓細鏋勯犲嚱鏁癋(x)=(1-x) * 鈭0鍒皒 f(t)dt锛屽垯F(x)鍦0,1涓婅繛缁紝鍦0,1鍐呭彲瀵硷紝F(0)=F(1)=0锛岀敱缃楀皵涓煎畾鐞嗭紝鍦0,1鍐呰嚦灏戝瓨鍦ㄤ竴鐐刮撅紝浣垮緱F'尉=0銆侳'(x)=- 鈭0鍒皒 f(t)dt+(1-x) * f(x)鎵浠'尉=- 鈭0鍒拔 f(t)dt+(1-尉) * f尉=0锛屽嵆鈭0鍒拔緁(x)dx=(1...
绛旓細^浠(x)=x^3*f(x)锛屽垯g(x)鍦╗0,1]涓婅繛缁紝鍦(0,1)鍐呭彲瀵 鍥犱负g(0)=0锛実(1)=f(1)=0锛屾墍浠ユ牴鎹綏灏斿畾鐞 瀛樺湪尉鈭(0,1)锛屼娇寰梘'(尉)=0 3尉^2*f(尉)+尉^3*f'(尉)=0 3f(尉)+尉f'(尉)=0 涓昏浼樺娍锛氬垯鍥犱负 f(a)=f(b) 浣垮緱鏈澶у M 涓庢渶灏忓 m 鑷冲皯鏈変竴涓...
绛旓細鐢辨媺鏍兼湕鏃ヤ腑鍊煎畾鐞嗙煡锛 瀛樺湪x1鈭(0,1/2),f'(x1)=[f(1/2)-f(0)]/(1/2)=2 x2鈭堬紙1/2,1),f'(x2)=[f(1)-f(1/2)]/(1/2)=-2 鐢卞鍑芥暟鐨勪腑闂村煎畾鐞嗗彲寰楋紝 瀛樺湪t鈭堬紙x1,x2),f'(t)=1 瀵煎嚱鏁板彇涓棿鍊煎畾鐞嗗強杈惧竷瀹氱悊銆傚叾璇佹槑鍙互鐧惧害銆
绛旓細浣滆緟鍔╁嚱鏁癵(x)=xf(x)锛屽垯g'(x)=f(x)+xf'(x)锛実(0)=g(1)=0锛屾牴鎹綏灏斿畾鐞嗭紝瀛樺湪a灞炰簬(0,1)浣垮緱g'(a)=f(a)+af'(a)=0锛屽嵆f'(a)=-f(a)/a銆
绛旓細鏋勯犲嚱鏁癋(x)=x²f(x)锛屽垯F(x)鍦╗0,1]涓婅繛缁紝鍦(0,1)鍐呭彲瀵硷紝F(0)=F(1)=0锛岀敱缃楀皵瀹氱悊锛屽瓨鍦ㄤ竴鐐刮锯垐(0,1)锛屼娇F'(尉)=0銆侳'(x)=2xf(x)+x²f'(x)銆傛墍浠ワ紝2尉f(尉)+尉²f'(尉)=0锛屾墍浠2f(尉)+尉f'(尉)=0銆
