应用麦克劳林公式,按x的幂展开函数f(x)=(x^2-3x+1)^3 应用麦克劳林公式
\u6309x\u7684\u5e42\u5c55\u5f00\u51fd\u6570f(x)=(x^2-3x+1)^3\u6c42\u51fan\u9636\u5bfc\uff0c\u7136\u540e\u5957\u516c\u5f0f\u5c31\u884c
\u9ea6\u514b\u52b3\u6797\u516c\u5f0f\u6309X\u7684\u5e42\u5c55\u5f00\u51fd\u6570\u662f\u6307\u5728x0=0\u5904\u5c55\u5f00.
\u5148\u6c42\u51fa
f (0) =1 ,f '(0) = -1 ,f ''(0) = -4/3 ,f '''(0) = -6 ,.\u4ee3\u5165\u6cf0\u52d2\u516c\u5f0f\u5f97\u5230\uff08\u5c55\u5f00\u52305\u6b21\u5e42\u65f6\uff09
f (x) = 1-x-2/3*x^2-x^3-16/9*x^4-31/9*x^5
求出n阶导，然后套公式就行
f(x)=x^6-9x^5+30x^4-39x^3+x^2-3x+1f(x)=f(0)+f'(0)x+[f''(0)/2!]+...+f"""(0)/6!
绛旓細銆愮瓟妗堛戯細f(x)=1-9x+30x2-45x3+30x4-9x5+x6
绛旓細楹﹀厠鍔虫灄鍏紡鎸塜鐨勫箓灞曞紑鍑芥暟鏄寚鍦▁0=0澶勫睍寮.鍏堟眰鍑 f (0) =1 ,f '(0) = -1 ,f ''(0) = -4/3 ,f '''(0) = -6 ,.浠ｅ叆娉板嫆鍏紡寰楀埌锛堝睍寮鍒5娆″箓鏃讹級f (x) = 1-x-2/3*x^2-x^3-16/9*x^4-31/9*x^5 ...
绛旓細鍥炵瓟锛歠(x)=x^6-9x^5+30x^4-39x^3+x^2-3x+1f(x)=f(0)+f'(0)x+[f''(0)/2!]+...+f"""(0)/6!
绛旓細f<6>(0)=720 f<n>(x)=0锛岋紙褰搉>6锛夋墍浠(x)=1+(-9)x+(60/2!)x^2+(-270/3!)x^3+(720/4!)x^4 +(-1080/5!)x^5+(720/6!)x^6 = 1 - 9x + 30x^2 - 45x^3 + 30x^4 - 9x^5 + x^6
绛旓細鎶婃煇鍑芥暟灞曞紑鎴 x 鐨勫箓绾ф暟鏃剁О涓楹﹀厠鍔虫灄灞曞紑锛岃屽睍寮鎴 x-x0 鐨勫箓绾ф暟鏃剁О涓娉板嫆灞曞紑锛屽墠鑰呮槸鍚庤呯殑鐗规畩鎯呭舰銆
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绛旓細sinx ~ x - x^3/3! + x^5/5! 鈥︹ 楹﹀厠鍔虫灄灞曞紡鍓3椤 e^x ~ 1+x+x^2/2!+x^3/3!+鈥︹﹀垎姣嶆槸 (sinx)^3 ~ x^3, 鎵浠ュ垎瀛愰害鍏嬪姵鏋楀睍寮忎腑姣 x^3 楂橀樁鐨勬棤绌峰皬鐣ュ幓 鑻ュ垎瀛愬悎骞剁粨鏋滀负0锛屽垯楹﹀厠鍔虫灄灞曞紡鍙兘闇瑕佸鍙栦竴椤癸紝鏋侀檺鍙兘涓 0 ...
绛旓細鎶婂畠浠唬鍥炲紡(1)锛屽緱 閫氬父绉板紡(2)涓篺(x)鐨楹﹀厠鍔虫灄灞曞紑寮忔垨f(x)鍦▁=0澶勭殑骞傜骇鏁板睍寮寮忋傚紡(2)涓瓑鍙峰彸绔殑绾ф暟绉颁负f(x)鐨勯害鍏嬪姵鏋楃骇鏁版垨f(x)灞曞紑鎴x鐨勫箓绾ф暟銆傝嚦浜庨棶棰(2)銆傚彧瑕佽瘉鏄庡叾浣欓」婊¤冻 鍗冲彲(璇佹槑鐣)銆備笅闈㈣冭檻鍦ㄤ粈涔堟潯浠朵笅锛屽嚱鏁癴(x)鑳藉睍寮鎴愰害鍏嬪姵鏋楃骇鏁般傚彲瑙锛屾寜鍏紡 姹傚緱...
绛旓細Cosx鐨勯害鍏嬪姵鏋楀叕寮鏄寚锛屽皢cosx鎸夌収骞傜骇鏁灞曞紑鐨勮〃绀哄紡锛屽叾涓瓁琛ㄧず寮у害銆傚畠鐨勪竴鑸舰寮忎负 sum锛坣=0,鈭烇級锛-1锛塣n*锛坸^2n锛/锛2n锛夛紒銆傚叾瀹锛岄害鍏嬪姵鏋楀叕寮鏄竴涓潪甯告湁鐢ㄧ殑鏁板宸ュ叿锛屽彲浠ョ敤鏉ュ皢浠讳綍涓涓嚱鏁拌〃绀轰负骞傜骇鏁扮殑褰㈠紡銆傚叿浣撴潵璇达紝鍦ㄦ暟瀛︿腑锛屽箓绾ф暟鏄竴绉嶆棤闄愬椤瑰紡锛屽叾涓瘡涓椤归兘鍖呭惈涓涓...
绛旓細姹傚嚭n闃跺锛岀劧鍚庡鍏紡灏辫
