涓€銆佽€冭│鍏�(n猫i)瀹瑰拰瑕佹眰
锛堜竴锛夊嚱鏁�(sh霉)銆佹サ闄愩€侀€g簩(x霉)
1锛庣悊瑙e嚱鏁�(sh霉)鐨勬蹇�锛屾帉鎻″嚱鏁�(sh霉)鐨勮〃绀烘硶锛岃兘澶犳纰哄缓绔嬬啊鍠噳(y墨ng)鐢ㄥ晱椤屼腑鐨勫嚱鏁�(sh霉)闂�(gu膩n)绯伙紟
2锛庝簡瑙e嚱鏁�(sh霉)鏈夌晫鎬с€佸柈瑾�(di脿o)鎬�銆佸懆鏈熸€у拰濂囧伓鎬х殑姒傚康锛屽苟鑳界啛绶村垎鏋愬嚱鏁�(sh霉)鍦栧舰鐗瑰緛锛�
3锛庣悊瑙e京(f霉)鍚堝嚱鏁�(sh霉)銆佸垎娈靛嚱鏁�(sh霉)銆佸弽鍑芥暩(sh霉)浠ュ強闅卞嚱鏁�(sh霉)鐨勬蹇碉紟
4锛庢帉鎻″熀鏈垵绛夊嚱鏁�(sh霉)鐨勫畾缇�銆佹€ц唱(zh矛)浠ュ強鍦栧舰鐗瑰緛锛屼簡瑙e垵绛夊嚱鏁�(sh霉)鐨勬蹇碉紟
5锛庣悊瑙fサ闄愩€佸柈鍋�(c猫)妤甸檺鐨勫畾缇╁強鍏朵箣闁撶殑鐩镐簰闂�(gu膩n)绯伙紟
6锛庣啛绶存帉鎻℃サ闄愮殑鎬ц唱(zh矛)鍙婂洓鍓囬亱(y霉n)绠楁硶鍓囷紟
7锛庣啛绶存帉鎻″苟閬�(y霉n)鐢ㄦサ闄愮殑鍏╁€�(g猫)瀛樺湪鎬ф簴(zh菙n)鍓囦互鍙婂叐鍊�(g猫)閲嶈妤甸檺锛�
8锛庣悊瑙g劇绐皬閲�銆佺劇绐ぇ閲忕殑瀹氱京鍙婂叾涔嬮枔鐨勯棞(gu膩n)绯�锛屾帉鎻$劇绐皬閲忛殠鐨勬瘮杓冩柟娉�锛屾帉鎻℃サ闄愯垏鐒$灏忛噺鐨勯棞(gu膩n)绯�锛岃兘澶犳纰哄埄鐢ㄧ瓑鍍�(ji脿)鐒$灏忛噺姹傝В妤甸檺鍟忛锛�
9锛庣悊瑙e嚱鏁�(sh霉)閫g簩(x霉)銆佸柈鍋�(c猫)閫g簩(x霉)鐨勬蹇靛強鍏朵箣闁撶殑闂�(gu膩n)绯�锛岃兘澶犵啛绶存壘鍑哄嚱鏁�(sh霉)鐨勯枔鏂烽粸(di菐n)骞跺垽鏂峰叾椤炲瀷锛�
10锛庝簡瑙i€g簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍜屽垵绛夊嚱鏁�(sh霉)鐨勯€g簩(x霉)鎬э紝鐞嗚В骞惰兘鐔熺反鎳�(y墨ng)鐢ㄩ枆鍗€(q奴)闁撲笂閫g簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛堟湁鐣屾€�銆佹渶澶у€煎拰鏈€灏忓€煎畾鐞�銆佷粙鍊煎畾鐞嗭級锛�
锛堜簩锛変竴鍏冨嚱鏁�(sh霉)寰垎瀛�(xu茅)
1锛庣悊瑙e皫(d菐o)鏁�(sh霉)銆佸柈鍋�(c猫)灏�(d菐o)鏁�(sh霉)銆佸井鍒嗙殑姒傚康锛岀悊瑙e皫(d菐o)鏁�(sh霉)鑸囧柈鍋�(c猫)灏�(d菐o)鏁�(sh霉)銆佸皫(d菐o)鏁�(sh霉)鑸囧井鍒嗙殑闂�(gu膩n)绯�锛屾帉鎻″皫(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇╁苟鑳芥帹灏�(d菐o)骞抽潰鏇茬窔鐨勫垏绶氭柟绋嬪拰娉曠窔鏂圭▼锛屼簡瑙e皫(d菐o)鏁�(sh霉)鐨勭墿鐞嗘剰缇�锛岃兘澶犲埄鐢ㄥ皫(d菐o)鏁�(sh霉)鎻忚堪涓€浜涚啊鍠殑鐗╃悊鐝�(xi脿n)璞★紝鐞嗚В鍑芥暩(sh霉)鐨勫彲灏�(d菐o)鎬ц垏閫g簩(x霉)鎬т箣闁撶殑闂�(gu膩n)绯伙紟
2锛庣啛绶存帉鎻″皫(d菐o)鏁�(sh霉)鐨勫洓鍓囬亱(y霉n)绠楁硶鍓�銆佸京(f霉)鍚堝嚱鏁�(sh霉)鐨勬眰灏�(d菐o)娉曞墖浠ュ強鍙嶅嚱鏁�(sh霉)鐨勬眰灏�(d菐o)鏂规硶锛屾帉鎻″熀鏈垵绛夊嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)鍏紡锛庣啛绶存帉鎻″井鍒嗙殑鍥涘墖閬�(y霉n)绠楁硶鍓囷紝鐞嗚В骞惰兘鎳�(y墨ng)鐢ㄥ嚱鏁�(sh霉)鐨勪竴闅庡井鍒嗗舰寮忎笉璁婃€�锛岀啛绶存帉鎻℃眰瑙e嚱鏁�(sh霉)寰垎鐨勬柟娉曪紟
3锛庣悊瑙i珮闅庡皫(d菐o)鏁�(sh霉)鐨勬蹇碉紝鐔熺反鎺ㄥ皫(d菐o)绨″柈鍑芥暩(sh霉)鐨勯珮闅庡皫(d菐o)鏁�(sh霉)锛�
4锛庢帉鎻″垎娈靛嚱鏁�(sh霉)銆侀毐鍑芥暩(sh霉)銆佺敱鍙冩暩(sh霉)鏂圭▼鎵€纰哄畾鐨勫嚱鏁�(sh霉)浠ュ強鍙嶅嚱鏁�(sh霉)灏�(d菐o)鏁�(sh霉)鐨勬眰瑙f柟娉曪紟
5锛庣悊瑙e苟鏈�(hu矛)鎳�(y墨ng)鐢ㄧ緟鐖撅紙Rolle锛夊畾鐞�銆佹媺鏍兼湕鏃ワ紙Lagrange锛変腑鍊煎畾鐞�銆佹煰瑗�( Cauchy锛変腑鍊煎畾鐞嗭紟
6锛庣啛绶存帉鎻℃噳(y墨ng)鐢ㄦ礇蹇呴仈(d谩)娉曞墖姹傝В鏈畾寮忔サ闄愶紟
7锛庣悊瑙e嚱鏁�(sh霉)鐨勬サ鍊笺€佹渶鍊间互鍙婃サ鍊奸粸(di菐n)銆佹渶鍊奸粸(di菐n)鐨勬蹇�锛屾帉鎻″嚱鏁�(sh霉)鍠(di脿o)鎬х殑鍒ゅ垾鏂规硶锛屾帉鎻℃眰瑙e嚱鏁�(sh霉)妤靛€奸粸(di菐n)鍜屾サ鍊煎苟鍒ゅ垾鏈€鍊煎拰鏈€鍊奸粸(di菐n)鐨勬柟娉曪紟
8锛庢帉鎻″嚱鏁�(sh霉)鍦栧舰鍑瑰嚫鎬х殑鍒ゅ垾鏂规硶锛屾渻(hu矛)姹傚嚱鏁�(sh霉)鍦栧舰鐨勬嫄榛�(di菐n)浠ュ強姘村钩銆侀墰鐩村拰鏂滄几杩戠窔锛屾渻(hu矛)绻埗鍑芥暩(sh霉)鐨勫湒褰紟
锛堜笁锛変竴鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)
1锛庣悊瑙e師鍑芥暩(sh霉)銆佷笉瀹氱⿳鍒嗗拰瀹氱⿳鍒嗙殑姒傚康锛�
2锛庣啛绶存帉鎻¤▓(j矛)绠椾笉瀹氱⿳鍒嗙殑鍩烘湰鍏紡锛屾帉鎻′笉瀹氱⿳鍒嗗拰瀹氱⿳鍒嗙殑鎬ц唱(zh矛)鍙婂畾绌嶅垎涓€煎畾鐞嗭紝鎺屾彙鎻涘厓绌嶅垎娉曡垏鍒嗛儴绌嶅垎娉曪紟
3锛庢渻(hu矛)姹傝В鏈夌悊鍑芥暩(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)銆佹湁鐞嗗紡鍜岀啊鍠劇鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒嗭紟
4锛庣悊瑙h畩闄愮⿳鍒嗭紙绌嶅垎涓婇檺鍑芥暩(sh霉)锛夊強鍏舵眰灏�(d菐o)鏂规硶锛屾帉鎻$墰闋撲竴钀婂竷灏艰尐鍏紡锛�
5锛庣悊瑙e弽甯哥⿳鍒嗙殑姒傚康锛屾渻(hu矛)瑷�(j矛)绠楀弽甯哥⿳鍒嗭紟
6锛庢帉鎻$敤瀹氱⿳鍒嗚〃閬�(d谩)鍜岃▓(j矛)绠椾竴浜涘咕浣曢噺鑸囩墿鐞嗛噺锛堝钩闈㈠湒褰㈢殑闈㈢⿳銆佸钩闈㈡洸绶氱殑寮ч暦銆佹棆杞�(zhu菐n)楂旂殑楂旂⿳鍙婂伌(c猫)闈㈢⿳銆佸钩琛屾埅闈㈤潰绌嶇偤宸茬煡鐨勭珛楂旈珨绌嶃€佸姛銆佸紩鍔�銆佸鍔涚瓑锛夊強鍑芥暩(sh霉)鐨勫钩鍧囧€硷紟
锛堝洓锛夊鍏冨嚱鏁�(sh霉)寰⿳鍒嗗(xu茅)
1锛庝簡瑙e鍏冨嚱鏁�(sh霉)鐨勬蹇�锛屼簡瑙d簩鍏冨嚱鏁�(sh霉)鐨勫咕浣曟剰缇╋紟
2锛庣悊瑙d簩鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫g簩(x霉)鐨勬蹇典互鍙婃湁鐣岄枆鍗€(q奴)鍩熶笂浜屽厓閫g簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛�
3锛庣悊瑙e鍏冨嚱鏁�(sh霉)鍋忓皫(d菐o)鏁�(sh霉)鐨勬蹇靛苟鑳界啛绶存眰瑙e鍏冨京(f霉)鍚堝嚱鏁�(sh霉)鐨勫悇闅庡亸灏�(d菐o)鏁�(sh霉)锛屾帉鎻″叏寰垎鐨勬蹇靛苟鑳界啛绶存眰瑙e鍏冨嚱鏁�(sh霉)鐨勫叏寰垎锛岀悊瑙i毐鍑芥暩(sh霉)瀛樺湪瀹氱悊骞舵渻(hu矛)姹傝В澶氬厓闅卞嚱鏁�(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉)锛�
4锛庣悊瑙e鍏冨嚱鏁�(sh霉)妤靛€煎拰姊濅欢妤靛€肩殑姒傚康锛屾帉鎻″鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑蹇呰姊濅欢锛岀悊瑙d簩鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑鍏呭垎姊濅欢骞舵眰瑙d簩鍏冨嚱鏁�(sh霉)鐨勬サ鍊�锛屾渻(hu矛)鐢ㄦ媺鏍兼湕鏃ヤ箻鏁�(sh霉)娉曟眰瑙e嚱鏁�(sh霉)姊濅欢妤靛€硷紝鏈�(hu矛)姹傜啊鍠鍏冨嚱鏁�(sh霉)鐨勬渶澶у€煎拰鏈€灏忓€�锛屽苟鏈�(hu矛)瑙f焙涓€浜涚啊鍠殑鎳�(y墨ng)鐢ㄥ晱椤岋紟
5锛庝簡瑙d簩閲嶇⿳鍒嗙殑姒傚康鑸囧熀鏈€ц唱(zh矛)锛屾帉鎻′簩閲嶇⿳鍒嗙殑瑷�(j矛)绠楁柟娉曪紙鐩磋鍧愭(bi膩o)銆佹サ鍧愭(bi膩o)锛夛紟
锛堜簲锛夌劇绐礆鏁�(sh霉)
1锛庣悊瑙g礆鏁�(sh霉)鏀舵杺鑸囩櫦(f膩)鏁�銆佹敹鏂傜礆鏁�(sh霉)鍜岀殑姒傚康锛�
2锛庢帉鎻$礆鏁�(sh霉)鐨勫熀鏈€ц唱(zh矛)鍜岀礆鏁�(sh霉)鏀舵杺鐨勫繀瑕佹浠讹紝鎺屾彙骞句綍绱氭暩(sh霉)鍙妏绱氭暩(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁g殑姊濅欢锛屾帉鎻℃闋�(xi脿ng)绱氭暩(sh霉)鏀舵杺鎬х殑姣旇純鍒ゅ垾娉曞拰姣斿€煎垽鍒ユ硶锛�
3锛庣悊瑙d换鎰忛爡(xi脿ng)绱氭暩(sh霉)绲曞皪鏀舵杺銆佹浠舵敹鏂傜殑姒傚康浠ュ強绲曞皪鏀舵杺鑸囨敹鏂傜殑闂�(gu膩n)绯�锛屼簡瑙d氦閷�(cu貌)绱氭暩(sh霉)鐨勮悐甯冨凹鑼ㄥ垽鍒ユ硶锛�
4锛庢帉鎻″啰绱氭暩(sh霉)鏀舵杺鍗婂緫銆佹敹鏂傚崁(q奴)闁撳強鏀舵杺鍩熺殑姒傚康鑸囨眰瑙f柟娉曪紟
5锛庣悊瑙e啰绱氭暩(sh霉)鍦ㄥ叾鏀舵杺鍗€(q奴)闁撳収(n猫i)鐨勫熀鏈€ц唱(zh矛)锛堝拰鍑芥暩(sh霉)鐨勯€g簩(x霉)鎬�銆侀€愰爡(xi脿ng)姹傚皫(d菐o)鍜岄€愰爡(xi脿ng)绌嶅垎锛夛紝骞舵眰瑙g啊鍠啰绱氭暩(sh霉)鍦ㄥ叾鏀舵杺鍗€(q奴)闁撳収(n猫i)鐨勫拰鍑芥暩(sh霉)锛�
6锛庢帉鎻x锛�sin x 锛�cos x 锛�ln(1+x) 鍙�(1+x)伪 鐨勯亥鍏嬪嫗鏋楋紙Maclaurin锛夊睍闁嬪紡锛�
锛堝叚锛夊父寰垎鏂圭▼
1锛庣悊瑙e井鍒嗘柟绋嬪強鍏堕殠銆佽В銆侀€氳В銆佸垵濮嬫浠跺拰鐗硅В绛夋蹇碉紟
2锛庢帉鎻¤畩閲忓彲鍒嗛洟鐨勫井鍒嗘柟绋嬶紟榻婃寰垎鏂圭▼鍜屼竴闅庣窔鎬у井鍒嗘柟绋嬬殑姹傝В鏂规硶锛�
3锛庢帉鎻℃眰瑙d簩闅庡父绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋嬶紟
4锛庣悊瑙g窔鎬у井鍒嗘柟绋嬭В鐨勬€ц唱(zh矛)鍙婅В鐨勭祼(ji茅)妲�(g貌u)瀹氱悊锛岃兘澶犳眰瑙h嚜鐢遍爡(xi脿ng)鐐哄闋�(xi脿ng)寮�銆佹寚鏁�(sh霉)鍑芥暩(sh霉)銆佹寮﹀嚱鏁�(sh霉)銆佷綑寮﹀嚱鏁�(sh霉)鐨勪簩闅庡父绯绘暩(sh霉)闈為綂娆$窔鎬у井鍒嗘柟绋嬶紟
5锛庤兘澶犻亱(y霉n)鐢ㄥ井鍒嗘柟绋嬫眰瑙g啊鍠噳(y墨ng)鐢ㄥ晱椤岋紟
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