涓€銆佺壒鍊兼硶

        椤у悕鎬濈京锛岀壒鍊兼硶灏辨槸鎵句竴浜涚鍚堥鐩姹傜殑鐗规畩姊濅欢瑙ｉ銆�

        渚嬶細f(n)=(n+1)^n-1锛坣鐐鸿嚜鐒舵暩(sh霉)涓攏锛�1锛夛紝鍓噁(n)

        锛圓锛夊彧鑳借n鏁撮櫎 锛圔锛夎兘琚玭^2鏁撮櫎 锛圕锛夎兘琚玭^3鏁撮櫎 锛圖锛夎兘琚�(n+1)鏁撮櫎 锛圗锛堿銆丅銆丆銆丏鍧囦笉姝ｇ⒑

        瑙ｇ瓟锛氫护n=2鍜�3锛屽嵆鍙珛鍗崇櫦(f膩)鐝�(xi脿n)f(2)=8锛宖(3)=63锛屼簬鏄煡A銆丆銆丏鍧囬尟瑾わ紝鑰屽皪浜庣洰鍓嶄簲閬镐竴鐨勯鍨�锛孍澶у鎯呮硜涓嬮兘鏄偤浜嗘箠浜斿€嬮伕闋呰€屼締鐨�锛屾墍浠�锛屼竴鑸彲浠ヤ笉鑰冩叜E锛屾墍浠�锛岄Μ涓婂氨鍙互寰楀嚭绛旀鐐築銆�

        渚嬶細鍦ㄧ瓑宸暩(sh霉)鍒梴an}涓�锛屽叕宸甦≠0锛屼笖a1銆乤3銆乤9鎴愮瓑姣旀暩(sh霉)鍒�锛屽墖(a1+a3+a9)/(a2+a4+a10)绛変簬

        锛圓锛�13/16 锛圔锛�7/8 锛圕锛�11/16 锛圖锛�-13/16 锛圗锛堿銆丅銆丆銆丏鍧囦笉姝ｇ⒑

        瑙ｇ瓟锛氬彇鑷劧鏁�(sh霉)鍒楋紝鍓囨墍姹傜偤(1+3+9)/(2+4+10)锛岄伕A銆�

        渚嬶細C(1,n)+3C(2,n)+3^2C(3,n)+……+3^(n-1)C(n,n)绛変簬

        锛圓锛�4^n 锛圔锛�3*4^n 锛圕锛�1/3*(4^n-1) 锛圖锛�4^n/3-1 锛圗锛堿銆丅銆丆銆丏鍧囦笉姝ｇ⒑

        瑙ｇ瓟锛氫护n=1锛屽墖鍘熷紡=1锛屽皪鎳変笅闈㈢瓟妗堢偤D銆�

        渚嬶細宸茬煡abc=1锛屽墖a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)绛変簬

        锛圓锛�1 锛圔锛�2 锛圕锛�3/2 锛圖锛�2/3 锛圗锛堿銆丅銆丆銆丏鍧囦笉姝ｇ⒑

        瑙ｇ瓟锛氫护a=b=c=1锛屽緱绲�(ji茅)鏋滅偤1锛屾晠閬窤銆�

        渚嬶細宸茬煡A鐐簄闅庢柟闄�锛孉^5=0锛孍鐐哄悓闅庡柈浣嶉櫍锛屽墖

        锛圓锛墊A|锛�0 锛圔锛墊A|锛�0 锛圕锛墊E-A|=0 锛圖锛墊E-A|≠0 锛圗锛堿銆丅銆丆銆丏鍧囦笉姝ｇ⒑

        瑙ｇ瓟锛氫护A=0锛堝嵆闆剁煩闄ｏ級锛岄Μ涓婂彲鐭銆丅銆丆鐨嗛尟锛屾晠閬窪銆�

        浜�銆佷唬鍏ユ硶

        浠ｅ叆娉�锛屽嵆寰為伕闋呭叆鎵�锛屼唬鍏ュ凡鐭ョ殑姊濅欢涓В椤屻€�

        渚嬶細绶氭€ф柟绋嬬祫

        x1+x2+λx3=4

        -x1+λx2+x3=λ^2

        x1-x2+2x3=-4

        鏈夊敮涓€瑙�

        锛�1顥傛仌?1 锛�2顥傛仌?

        瑙ｇ瓟锛氬皪鍚弮鏁�(sh霉)鐨勭煩闄ｉ€茶鍒濈瓑琛岃畩鎻涢洠鍏嶆湁浜涘京闆�锛岃€屼笖瀹规槗鍑洪尟锛屽鏋滅洿鎺ユ妸涓嬮潰鐨勫€间唬鍏ユ柟绋�锛屽垽鏂锋槸鍚︽豢瓒虫湁鍞竴瑙ｏ紝灏辫鏂逛究寰楀銆傜瓟妗堟槸閬窩銆�

        渚嬶細涓嶇瓑寮�5≤|x^2-4|≤x+2鎴愮珛

        锛�1锛墊x|锛�2 锛�2锛墄锛�3

        瑙ｇ瓟锛氫笉闇€瑕佽В涓嶇瓑寮�锛岃€屾槸灏囨浠讹紙1锛�銆侊紙2锛変腑鎵句竴鍊嬪€紉=2.5锛屾渻棣笂鐧�(f膩)鐝�(xi脿n)涓嶇瓑寮忔槸涓嶆垚绔嬬殑锛屾墍浠ラ伕E銆�

        渚嬶細琛屽垪寮�

        1 0 x 1

        0 1 1 x =0

        1 x 0 1

        x 1 1 0

        锛�1锛墄=±2 锛�2锛墄=0

        瑙ｇ瓟锛氱洿鎺ユ妸姊濅欢锛�1锛�銆侊紙2锛変唬鍏ラ鐩�锛屽彲鐧�(f膩)鐝�(xi脿n)绲�(ji茅)璜栧潎鎴愮珛锛屾墍浠ラ伕D銆�

        涓�銆佸弽渚嬫硶

        鎵句竴鍊嬪弽渚嬪湪鎺ㄥ€掗鐩殑绲�(ji茅)璜�锛岄€欎篃鏄稉(j墨ng)甯哥敤鍒扮殑鏂规硶銆傞€氬父锛屽弽渚嬮伕鎿囦竴浜涘緢甯歌鐨勬暩(sh霉)鍊�銆�

        渚嬶細A銆丅鐐簄闅庡彲閫嗙煩闄�锛屽畠鍊戠殑閫嗙煩闄ｅ垎鍒ユ槸A^T銆丅^T锛屽墖鏈墊A+B|=0

        锛�1锛墊A|=-|B| 锛�2锛墊A|=|B|

        瑙ｇ瓟锛氬皪浜庢浠讹紙2锛�锛屽鏋淎=B=E鐨勮┍锛岄’鐒堕鐩殑绲�(ji茅)璜栨槸涓嶆垚绔嬬殑锛岄€欏氨鏄竴鍊嬪弽渚�锛屾墍浠ユ渶鍚庣殑绛旀锛屽氨鍙渶鑰冩叜A鎴朎浜�銆�

        渚嬶細绛夊紡x^2/a^2+y^2/b^2+z^2/c^2=1鎴愮珛

        锛�1锛塧^2+b^2+c^2=x^2+y^2+z^2 锛�2锛墄/a+y/b+z/c=1锛屼笖a/x+b/y+c/z=0

        瑙ｇ瓟锛氬皪浜庢浠讹紙1锛�锛岃嫢a=b=c=x=y=z=1锛岄’鐒堕鐩殑绲�(ji茅)璜栨槸涓嶆垚绔嬬殑銆傛墍浠ワ紝鏈€鍚庣殑绛旀锛屽氨鍙渶瑕佽€冩叜B銆丆鎴朎浜�銆�

        鍥�銆佽瀵熸硶

        瑙€瀵熸硶鐨勬剰鎬�锛屽氨鏄緸椤岀洰鐨勬浠跺拰閬搁爡涓洿鎺ヨ瀵�锛屽緱鍑虹祼(ji茅)璜栨垨鍙互鎺掗櫎鐨勯伕闋�銆�

        渚嬶細瑷洸绶歽=y(x)鐢辨柟绋�(1-y)/(1+y)+ln(y-x)=x鎵€纰哄畾锛屽墖閬庨粸(0,1)鐨勫垏绶氭柟绋嬬偤

        锛圓锛墆=2x+1 锛圔锛墆=2x-1 锛圕锛墆=4x+1 锛圖锛墆=4x-1 锛圗锛墆=x+2

        瑙ｇ瓟锛氬洜鍒囩窔閬庨粸(0,1)锛屽皣x=0銆亂=1浠ｅ叆浠ヤ笅鏂圭▼锛屽嵆鍙洿鎺ユ帓闄銆丏鍜孍銆�

        渚嬶細涓嶇瓑寮�(|x-1|-1)/|x-3|锛�0鐨勮В闆嗙偤

        锛圓锛墄锛�0 锛圔锛墄锛�0鎴杧锛�2 锛圕锛�-3锛渪锛�0鎴杧锛�2 锛圖锛墄锛�0鎴杧锛�2涓攛≠3 锛圗锛堿銆丅銆丆銆丏鍧囦笉姝ｇ⒑

        瑙ｇ瓟锛氬緸椤岀洰鍙湅鍑�锛寈涓嶈兘绛変簬3锛屾墍浠ワ紝閬搁爡B銆丆鍧囦笉姝ｇ⒑锛屽彧鍓╀笅A鍜孌锛屽啀鎵句竴鍊嬬壒鍊间唬鍏�锛屽嵆鍙緱D鐐烘纰虹瓟妗�銆�

        渚嬶細鍏锋湁浠ヤ笅鐨勬€ц唱(zh矛)锛氾紙1锛夊畠鐨勫皪绋辫桓骞宠浜巠杌�锛屼笖鍚戜笂褰�锛涳紙2锛夊畠鑸噚杌告墍鍦嶇殑闈㈢⿳鏈€灏�锛屼笖閫氶亷(0,0)锛�(1,-2)鐨勬媼鐗╃窔鐐�

        锛圓锛墆=4x^2-6x 锛圔锛墆=2x^2-3x 锛圕锛墆=4x^2-3x 锛圖锛墆=x^2-3x 锛圗锛墆=x^2-6x

        瑙ｇ瓟锛氭妸x=1銆亂=-2浠ｅ叆閬搁爡锛屽嵆鍙帓闄銆丆鍜孍銆�

        渚嬶細宸茬煡鏇茬窔鏂圭▼x^(y^2)+lny=1锛屽墖閬庢洸绶氫笂(1,1)榛炶檿鐨勫垏绶氭柟绋嬬偤

        锛圓锛墆=x+2 锛圔锛墆=2-x 锛圕锛墆=-2-x 锛圖锛墆=x-2 锛圗锛堿銆丅銆丆銆丏鍧囦笉姝ｇ⒑

        瑙ｇ瓟锛氬皣 x=1銆亂=1浠ｅ叆閬搁爡锛屽嵆鍙櫦(f膩)鐝�(xi脿n)B鐐烘纰虹瓟妗堛€�

        浜�銆�缍�(j墨ng)椹�娉�

        缍�(j墨ng)椹楁硶锛岄€氬父鍦ㄥ垵绛�鏁�(sh霉)瀛�鐨勫厖鍒嗘浠舵€у垽鏂烽涓娇鐢紝涓€鑸殑鎯呮硜鏄緢椤劧鑳界湅鍑哄叐鍊嬫浠跺柈鐛ㄥ潎涓嶅厖鍒�锛岃€岃伅(li谩n)绔嬭捣渚嗘湁鍙兘鏄瓟妗�锛岄€欐檪锛岀瓟妗堝ぇ澶氱偤C銆�

        渚嬶細瑕佷娇澶у皬涓嶇瓑鐨勫叐鏁�(sh霉)涔嬪拰鐐�20

        锛�1锛夊皬鏁�(sh霉)鑸囧ぇ鏁�(sh霉)涔嬫瘮鐐�2:3锛�

        锛�2锛夊皬鏁�(sh霉)鑸囧ぇ鏁�(sh霉)鍚勫姞涓�10涔嬪悗鐨勬瘮鐐�9:11

        渚嬶細鏀归潻鍓嶆煇鍦嬬嚐浼佹キ(y猫)骞翠汉鍧囩敘(ch菐n)鍊兼笡灏�40%

        锛�1锛夊勾绺界敘(ch菐n)鍊兼笡灏�25% 锛�2锛夊勾鍝″伐绺芥暩(sh霉)澧炲姞25%

        渚嬶細鐢�銆佷箼鍏╀汉鍚堣卜姗樺瓙锛岃兘纰哄畾姣忓€嬫瀛愮殑鍍归將鐐�0.4鍏�

        锛�1锛夌敳寰楁瀛�23鍊�锛屼箼寰楁瀛�17鍊�

        锛�2锛夌敳銆佷箼鍏╀汉骞冲潎鍑洪將璨锋瀛愶紝鍒嗘瀛愬悗锛岀敳鍙堢郸涔�1.2鍏�

        渚嬶細璨�1瑙掑拰5瑙掔殑閮电エ鐨勫嫉鏁�(sh霉)涔嬫瘮鐐�(10a-5b) : (10a+b)

        锛�1锛夎卜閮电エ鍏辫姳a鍏� 锛�2锛�5瑙掗兊绁ㄦ瘮1瑙掗兊绁ㄥ璨穊寮�

        渚嬶細鏌愬競鐝�(xi脿n)鏈夐儕鍗€(q奴)浜哄彛28钀汉

        锛�1锛夎┎甯傜従(xi脿n)鏈変汉鍙�42钀汉 锛�2锛夎┎甯傝▓鍔冧竴骞村悗鍩庡崁(q奴)浜哄彛澧為暦0.8%锛岄儕鍗€(q奴)浜哄彛澧為暦1.1%锛岃嚧浣垮叏甯備汉鍙ｅ闀�1%

        鍏�銆佸湒绀烘硶

        鐢ㄧ暙鍦栫殑鏂规硶瑙ｉ锛屽皪浜庝竴浜涢泦鍚堝拰绌嶅垎椤�锛岃兘璧峰埌浜嬪崐鍔熷€嶇殑鏁堟灉銆�

        渚嬶細鑻( B )=0.6锛孭( A+B )=0.7锛屽墖P(A|B璺嬶級=

        锛圓锛�0.1 锛圔锛�0.3 锛圕锛�0.25 锛圖锛�0.35 锛圗锛�0.1667

        瑙ｇ瓟锛氱暙鍑哄湒锛屽彲浠ュ緢蹇В鍑虹瓟妗堢偤C銆�

        渚嬶細A-( B-C )=( A-B )-C

        锛�1锛堿C=φ 锛�2锛塁鍖呭惈浜嶣

        瑙ｇ瓟锛氬悓妯ｉ倓鏄暙鍦�锛屽彲浠ョ煡閬撴纰虹瓟妗堢偤A銆�

        涓�銆佽挋鐚滄硶

        閫欐槸灞簬鏈€鍚庢矑鏈夋檪闁撶殑鎯呮硜锛屼娇鐢ㄧ殑涓€绋牬閲滄矇鑸熺殑鏂规硶?锛熸ⅱ鍏佺獌璇癈鍚堥亱鐢ㄤ互涓婃柟娉曠殑鍩虹涓�锛屽湪鎺掗櫎浠ュ鐨勯伕闋呬腑閫茶閬告搰銆傝€屽皪浜庡厖鍒嗘浠跺垽鏂烽渚嗚锛屾牴鎿�(j霉)缍�(j墨ng)椹�锛岄伕D鍜岄伕C鐨勬鐜囨瘮杓冨ぇ涓€浜�銆�

        涓冪ó姝﹀櫒灏遍€欎簺浜�銆備絾灏嶄簬鎴戝€戝闅涙噳瑭︿締瑾�锛屾洿澶氱殑閭勬槸鍦ㄦ帉鎻″熀鏈蹇电殑鍩虹涓婏紝鎴栬€呮椿瀛告椿鐢�锛屾垨鑰呮寜閮ㄥ氨鐝€備笉绠℃€庝箞瑾�锛屾垜鍊戣拷姹傞€熷害锛屾垜鍊戜篃杩芥眰璩�(zh矛)閲忋€�

        杩戜締锛屾湁浜涗汉鍦≦Q涓婃垨鑰�璜栧涓婂悜鎴戞墦鑱芥湁闂滃浣曞京缈掓暩(sh霉)瀛哥殑鍟忛锛屾垜鎯充簡涓€涓�锛岃寰楁湁浠ヤ笅骞鹃粸鍦ㄦ暩(sh霉)瀛哥殑寰╃繏鐣朵腑鏄渶瑕佹敞鎰忕殑锛�

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