姝¤繋瑷晱(w猫n)鑰冪爺绉樼睄鑰冪爺缍�(w菐ng)!    鐮旂┒鐢熸嫑鐢熶俊鎭恫(w菐ng)    鑰冨崥鐪熼涓嬭級    鑰冪爺鐪熼涓嬭級    鍏ㄧ珯鏂囩珷绱㈠紩
鏂囩珷鎼滅储
   
  楂樼礆(j铆)鎼滅储   

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銆€銆€绱�(j铆)鏁�(sh霉)涓€绔犵湅浼肩啊(ji菐n)鍠�锛屼絾瀵�(sh铆)闅涢渶瑕佹敞鎰忕殑鍦版柟涔熸瘮杓冪殑澶氾紝鐗瑰垾濡傗垜鐨勪笅妯�(bi膩o)鏄緸0闁嬪閭勬槸寰�1闁嬪锛焁鈭慤n涓殑X鍦ㄦ眰鍜屽嚱鏁�(sh霉)鏅�(sh铆)鏄斁鍦ㄧ⿳鍒嗙铏�(h脿o)涔嬪収(n猫i)鍛㈤倓鏄斁鍦ㄥ叾涔嬪锛熺瓑绛�锛岃薄閫欑ó绱�(x矛)寰殑宸垾灏辨湁鍙兘浣挎偍鐨勬眰瑙g祼(ji茅)鏋滅浉宸崄钀�(w脿n)鍏崈閲屻€備互涓嬫槸涓€浜涢棞(gu膩n)浜庢湰浜哄湪姹傝В绱�(j铆)鏁�(sh霉)瑭﹂鏅�(sh铆)鎵€浣滅殑鎶€宸у拰娉ㄦ剰榛�(di菐n)绺界祼(ji茅)锛岀湅涓€涓嬫偍鏄惁鏇剧稉(j墨ng)涔熺姱閬�(gu貌)椤炰技鐨勯尟(cu貌)瑾�銆�

1锛夆垜锛�0锛屸垶锛塻in(a蟺)=鈭戯紙0锛屸垶锛�(-1)^nsin(a蟺-n蟺)

2锛夊湪閬�(y霉n)鐢ㄨ悐甯冨凹鑼插垽鏂傛硶鍓囨檪(sh铆)鐨勭浜屽€�(g猫)姊濅欢鍙互閬�(y霉n)鐢ㄥ柈瑾�(di脿o)鎬у垽鏂凤紱鍗砯'(x)鏄惁澶т簬0锛�

3锛夊湪瑙e睍闁嬪啰绱�(j铆)鏁�(sh霉)鎴栨眰鍐礆(j铆)鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鏅�(sh铆)锛屾敹鏂傚煙鐨勬眰瑙e嬁蹇�銆�

4锛夊湪鏌愰粸(di菐n)铏曞睍闁嬪啰绱�(j铆)鏁�(sh霉)闄や簡瀵嚭鏀舵杺鍩熷閭勮鍘婚櫎瑭查粸(di菐n)銆�

5锛夊湪瑙e啰绱�(j铆)鏁�(sh霉)灞曢枊鏅�(sh铆)鎳�(y墨ng)娉ㄦ剰锛屸垜鐨勪笅妯�(bi膩o)鏄緸0闁嬪閭勬槸寰�1闁嬪锛屽湪鍏锋湁绌嶅垎鏅�(sh铆)閭勯渶鐪媐(0)鏄惁鐐�0銆傚嵆鈭玣'(x)dx+f(0)=f(x).閫欎竴榛�(di菐n)浣滀簡鏂扮殑淇▊

6锛夊湪姹傚啰绱�(j铆)鏁�(sh霉)鍜屽嚱鏁�(sh霉)鏅�(sh铆)锛岀⿳鍒�锛屽皫(d菐o)鏁�(sh霉)鏃㈠彲灏�(du矛)鈭戝収(n猫i)鐨刋璧蜂綔鐢�锛屼篃鍙互灏�(du矛)鈭戝鐨刋璧蜂綔鐢紝浣嗛渶瑕佷竴涓€灏�(du矛)鎳�(y墨ng)锛屽嵆灏�(du矛)琚檿鐞嗛爡(xi脿ng)鐢ㄤ竴娆$⿳鍒嗗悓鏅�(sh铆)蹇呴爤灏�(du矛)鍏剁敤涓€娆″皫(d菐o)鏁�(sh霉)锛涘弽涔嬩篃鐒躲€�

7锛夋眰寰楀拰鍑芥暩(sh霉)琛ㄩ仈(d谩)寮忔檪(sh铆)锛岄倓瑕佺湅灞簬鏀舵杺鍩�锛屼絾骞朵笉灞簬瀹氱京鍩熺殑榛�(di菐n)锛岄€欎簺榛�(di菐n)闇€瑕佸柈鐛�(d煤)鍒楀嚭渚�(l谩i)锛屾眰寰楀拰鍑芥暩(sh霉)鐨勫€�銆�

8锛夌暥(d膩ng)鈭戯紙0锛屸垶锛塙n涓殑U0=0鏅�(sh铆)锛屸垜锛�0锛屸垶锛塙n=鈭戯紙1锛屸垶锛塙n锛岃€屼笖鍦ㄥ鐢ㄧ⿳鍒嗘檪(sh铆)蹇呴爤瀵垚鍚庤€呭舰寮�锛屼互鍏嶅嚭鐝�(xi脿n)鈭�(0,x)0dx=1鐨勯尟(cu貌)瑾ゆ儏娉�銆傛敞鎰忥細鏈夌殑涓嬭〃鐢氳嚦寰�2闁嬪銆傚闄炽€婂京(f霉)缈�(x铆)鎸囧崡銆�02鐗堜緥8锛�31,(2)

9锛夋暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)姹傚拰鐨勫洓椤炴柟娉曪細绨�(ji菐n)鍠綁(zhu菐n)鎻涙硶锛屾媶闋�(xi脿ng)鐩告秷娉曪紝閬炴帹娉�锛岄樋鐖捐矟娉曘€傚叾涓樋鐖捐矟娉曟渶閲嶈銆�

10锛夋眰瑙e倕绔嬭憠绱�(j铆)鏁�(sh霉)鏅�(sh铆)鐨勫洓榛�(di菐n)绺界祼(ji茅)
a銆佸皪(du矛)浜庝竴鍊�(g猫)绱�(j铆)鏁�(sh霉)鏃㈠彲浠ュ闁嬫嫇锛屽張鍙互鍋堕枊鎷�锛屾寜椤岀洰鐨勮姹傜⒑瀹氭眰姝e鸡绱�(j铆)鏁�(sh霉)閭勬槸浣欏鸡绱�(j铆)鏁�(sh霉)
b銆侀枊鎷撳悗鐨勭礆(j铆)鏁�(sh霉)鎸夊钩甯哥礆(j铆)鏁�(sh霉)灞曢枊锛屽苟娉ㄦ剰瀵笂瀹氱京鍩�
c銆佸畾缇╁煙鐨勭榛�(di菐n)鐨勫倕绔嬭憠绱�(j铆)鏁�(sh霉)鏄矑(m茅i)鏈夋剰缇╃殑锛屽瑕佹眰鍊�锛屽墖闇€鐢ㄧ媱钀婂厠鍒╁畾鐞嗘眰瑙�
d銆佸湪姹俛n鎴朾n鏅�(sh铆)鍑虹従(xi脿n)[1-(-1)^n]閫欐ǎ鐨勯爡(xi脿ng)鏅�(sh铆)锛屼竴鑸儏娉佷笅浣縩=2k,n=2k+1鍒嗛枊瑷庤珫锛屼娇绲�(ji茅)鏋滄洿绨�(ji菐n)娼�


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棣栧厛鍒ゆ柗绱�(j铆)鏁�(sh霉)鐨勯鍨�

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