銆€銆€绱氭暩(sh霉)涓€绔犵湅浼肩啊鍠�锛屼絾瀵﹂殯闇€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欐槸寰�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)鏅傛槸鏀惧湪绌嶅垎绗﹁櫉涔嬪収(n猫i)鍛㈤倓鏄斁鍦ㄥ叾涔嬪锛熺瓑绛�锛岃薄閫欑ó绱板井鐨勫樊鍒ュ氨鏈夊彲鑳戒娇鎮ㄧ殑姹傝В绲�(ji茅)鏋滅浉宸崄钀叓鍗冮噷銆備互涓嬫槸涓€浜涢棞(gu膩n)浜庢湰浜哄湪姹傝В绱氭暩(sh霉)瑭﹂鏅傛墍浣滅殑鎶€宸у拰娉ㄦ剰榛炵附绲�(ji茅)锛岀湅涓€涓嬫偍鏄惁鏇剧稉(j墨ng)涔熺姱閬庨浼肩殑閷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锛夊湪閬嬬敤钀婂竷灏艰尣鍒ゆ杺娉曞墖鏅傜殑绗簩鍊嬫浠跺彲浠ラ亱鐢ㄥ柈瑾�(di脿o)鎬у垽鏂�锛涘嵆f'(x)鏄惁澶т簬0锛�

3锛夊湪瑙ｅ睍闁嬪啰绱氭暩(sh霉)鎴栨眰鍐礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鏅傦紝鏀舵杺鍩熺殑姹傝В鍕垮繕銆�

4锛夊湪鏌愰粸铏曞睍闁嬪啰绱氭暩(sh霉)闄や簡瀵嚭鏀舵杺鍩熷閭勮鍘婚櫎瑭查粸銆�

5锛夊湪瑙ｅ啰绱氭暩(sh霉)灞曢枊鏅傛噳娉ㄦ剰锛屸垜鐨勪笅妯欐槸寰�0闁嬪閭勬槸寰�1闁嬪锛屽湪鍏锋湁绌嶅垎鏅傞倓闇€鐪媐(0)鏄惁鐐�0銆傚嵆鈭玣'(x)dx+f(0)=f(x).閫欎竴榛炰綔浜嗘柊鐨勪慨瑷�

6锛夊湪姹傚啰绱氭暩(sh霉)鍜屽嚱鏁�(sh霉)鏅�锛岀⿳鍒嗭紝灏庢暩(sh霉)鏃㈠彲灏嶁垜鍏�(n猫i)鐨刋璧蜂綔鐢�锛屼篃鍙互灏嶁垜澶栫殑X璧蜂綔鐢�锛屼絾闇€瑕佷竴涓€灏嶆噳锛屽嵆灏嶈铏曠悊闋呯敤涓€娆＄⿳鍒嗗悓鏅傚繀闋堝皪鍏剁敤涓€娆″皫鏁�(sh霉)锛涘弽涔嬩篃鐒�銆�

7锛夋眰寰楀拰鍑芥暩(sh霉)琛ㄩ仈寮忔檪锛岄倓瑕佺湅灞簬鏀舵杺鍩燂紝浣嗗苟涓嶅爆浜庡畾缇╁煙鐨勯粸锛岄€欎簺榛為渶瑕佸柈鐛ㄥ垪鍑轰締锛屾眰寰楀拰鍑芥暩(sh霉)鐨勫€�銆�

8锛夌暥鈭戯紙0锛屸垶锛塙n涓殑U0=0鏅�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⿳鍒嗘檪蹇呴爤瀵垚鍚庤€呭舰寮忥紝浠ュ厤鍑虹従(xi脿n)鈭�(0,x)0dx=1鐨勯尟瑾ゆ儏娉�銆傛敞鎰忥細鏈夌殑涓嬭〃鐢氳嚦寰�2闁嬪銆傚闄炽€婂京缈掓寚鍗椼€�02鐗堜緥8锛�31,(2)

9锛夋暩(sh霉)闋呯礆鏁�(sh霉)姹傚拰鐨勫洓椤炴柟娉曪細绨″柈杞�(zhu菐n)鎻涙硶锛屾媶闋呯浉娑堟硶锛岄仦鎺ㄦ硶锛岄樋鐖捐矟娉�銆傚叾涓樋鐖捐矟娉曟渶閲嶈銆�

10锛夋眰瑙ｅ倕绔嬭憠绱氭暩(sh霉)鏅傜殑鍥涢粸绺界祼(ji茅)
a銆佸皪浜庝竴鍊嬬礆鏁�(sh霉)鏃㈠彲浠ュ闁嬫嫇锛屽張鍙互鍋堕枊鎷擄紝鎸夐鐩殑瑕佹眰纰哄畾姹傛寮︾礆鏁�(sh霉)閭勬槸浣欏鸡绱氭暩(sh霉)
b銆侀枊鎷撳悗鐨勭礆鏁�(sh霉)鎸夊钩甯哥礆鏁�(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榛炵殑鍌呯珛钁夌礆鏁�(sh霉)鏄矑鏈夋剰缇╃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鏅傚嚭鐝�(xi脿n)[1-(-1)^n]閫欐ǎ鐨勯爡鏅�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℃綌

鍥爊anxingstar缍�(w菐ng)鍙嬬殑瑕佹眰锛屼互涓嬫槸濡備綍姹傜礆鏁�(sh霉)鏂傛暎鎬х殑绺界祼(ji茅)

濡備綍姹傜礆鏁�(sh霉)鐨勬杺鏁ｆ€э紙鎷垮埌涓€鍊嬫杺鏁ｆ€у垽鏂峰晱椤屾檪鎬庢ǎ鍏ユ墜锛�

棣栧厛鍒ゆ柗绱氭暩(sh霉)鐨勯鍨�

1锛屽鏋滅礆鏁�(sh霉)鐐烘闋呯礆鏁�(sh霉)锛氬墖鍏堢湅鐣秐瓒ㄤ簬鐒＄鏅俇n鏄惁绛変簬0锛屼笉鐐�0鍓囩礆鏁�(sh霉)鐧�(f膩)鏁�锛岀瓑浜�0鍓囩敤浠ヤ笅涓夌ó鏂规硶鍒ゆ柗
1锛夋瘮杓冩硶
2锛夋瘮鍊兼硶
3锛夋牴鍊兼硶

鎶€宸э細
1锛夊鏋滅礆鏁�(sh霉)闋呬腑鍚湁闅庝箻鐨勫舰寮忎竴鑸敤姣斿€兼硶
2锛夊鏋滅礆鏁�(sh霉)闋呬腑鍚湁鎸囨暩(sh霉)闋匬^n鍓囦竴鑸敤鏍瑰€兼硶
3锛夋棦鏈夐殠涔橀爡鍙堟湁鎸囨暩(sh霉)闋呭墖涓€鑸敤姣斿€兼硶
4锛夊叾瀹冪殑涓€鑸敤姣旇純娉�
a銆佸叐鍊嬪畾鐞�
宸舰寮忓拰妤甸檺褰㈠紡
b銆佸叐鍊嬫帹璜�
鏁�(sh霉)涔樺樊褰㈠紡鍜孭-绱氭暩(sh霉)褰㈠紡

2锛屽鏋滅礆鏁�(sh霉)鏄氦閷礆鏁�(sh霉)
鍓囬亱鐢ㄨ悐甯冨凹鑼插畾鐞�

鎶€宸э細
鍦ㄥ垽鏂风浜屽€嬫浠舵檪涓€鑸敤鍠(di脿o)鎬у垽鏂�

3锛屽鏋滄槸浠绘剰闋呯礆鏁�(sh霉)
鍓囪綁(zhu菐n)鍖栨垚姝ｉ爡绱氭暩(sh霉)锛岄亱鐢ㄤ换鎰忛爡绱氭暩(sh霉)鍜屾闋呯礆鏁�(sh霉)鐨勯棞(gu膩n)绯昏│鍒ゆ柗锛堝畾鐞嗕竷锛�

娉ㄦ剰榛烇細
1锛夋瘮鍊兼硶锛屾牴鍊兼硶鏄厖鍒嗕絾涓嶅繀瑕佹浠�
2锛夋秹鍙婅瓑鏄庝竴鑸彧鑳界敤姣旇純娉�
3锛変絾鍦ㄥ垽鏂风礆鏁�(sh霉)鐧�(f膩)鏁ｆ檪锛屾瘮鍊兼硶锛屾牴鍊兼硶鍚屾ǎ閬╃敤

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