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1
鐩寗
I 鑰冩煡鐩......................................................閷锛佹湭瀹氱京鏇哥敖銆�
II 鑰冭│褰㈠紡鍜岃│鍗风祼妲� ................................閷锛佹湭瀹氱京鏇哥敖銆�
III 鑰冩煡鍏�(n猫i)瀹�...................................................閷锛佹湭瀹氱京鏇哥敖銆�
IV. 椤屽瀷绀轰緥鍙婂弮鑰冪瓟妗�...............................閷锛佹湭瀹氱京鏇哥敖銆�
2
鍏ㄥ湅纰╁＋鐮旂┒鐢熷叆瀛哥当(t菕ng)涓€鑰冭│
楂樼瓑鏁�(sh霉)瀛歌€冭│澶х侗
I 鑰冩煡鐩
鐩殑鏄瀛�銆佸叕骞�銆佹湁鏁堝湴娓│鑰冪敓鏄惁鍏峰倷鏀昏畝鐩搁棞灏堟キ(y猫)纰╁＋鎵€蹇呴爤鐨勫熀鏈礌璩�銆佷竴
鑸兘鍔涘拰鍩归(y菐ng)娼涜兘锛屼互鍒╃敤閬告嫈鍏锋湁鐧�(f膩)灞�?ji茅)鎽课﹁啲?y艒u)绉€浜烘墠鍏ュ锛岀偤鍦嬪鐨勭稉(j墨ng)婵熷缓瑷煿椁�(y菐ng)鍏锋湁
杓冨挤鍒嗘瀽鑸囪В姹哄闅涘晱椤岃兘鍔涚殑楂樺堡娆�銆佹噳鐢ㄥ瀷銆佸京鍚堝瀷鐨勬潗鏂欐垚鍨嬪皥妤�(y猫)浜烘墠?锛熻崥鍤媦瑭﹁€�
鐢熸帉鎻′竴鍏冨嚱鏁�(sh霉)鍩烘湰姒傚康銆佸熀鏈€ц唱銆佸熀鏈悊璜栫殑鎵庡绋嬪害锛岃€冩煡鑰冪敓鑳界啛绶撮亱鐢ㄩ€欎簺姒傚康
鑸囩悊璜栧垎鏋愯В姹虹従(xi脿n)瀵︾敓鐢�(ch菐n)涓垏鍑芥暩(sh霉)鏈夐棞鏁�(sh霉)瀛稿晱椤岀殑鑳藉姏.
鍏烽珨渚嗚銆傝姹傝€冪敓锛�
鎺屾彙涓€鍏冨熀鏈垵绛夊嚱鏁�(sh霉)鐨勫畾缇┿€佸湒鍍�銆佸皫鏁�(sh霉)鍏紡銆佺⿳鍒嗗叕寮忥紱鏈冪敤妤甸檺銆佸皫鏁�(sh霉)鍜岀⿳鍒嗗伐
鍏峰拰鏂规硶渚嗙爺绌朵竴鍏冨嚱鏁�(sh霉)灞€閮ㄦ湁鐣屾€�銆佷繚铏熸€�銆佷繚涓嶇瓑寮忔€у拰鏁撮珨鏈夌晫鎬�銆佸柈瑾�(di脿o)鎬�銆佸嚫鍑规€�銆�
鏈€灏忓€�銆佹渶澶у€�銆佸崁(q奴)闁撲笂骞冲潎鍊肩瓑鍏ㄥ眬鎬ц唱銆傚悓鏅備篃鑳芥墍瀛稿皫鏁�(sh霉)鍜屽畾绌嶅垎鐭ヨ瓨渚嗛€茶寰垎鏂�
绋嬪缓妯″拰姹傝В銆�
II 鑰冭│褰㈠紡鍜岃│鍗风祼妲�
涓€銆佽│鍗锋豢鍒嗗強鑰冭│鏅傞枔
瑭﹀嵎婊垮垎鐐� 150 鍒�锛岃€冭│鏅傞枔 180 鍒嗛悩銆�
浜�銆佺瓟椤屾柟寮�
闁夊嵎銆佺瓎瑭︺€傚厑瑷变娇鐢ㄨ▓绠楀櫒锛屼絾涓嶅緱浣跨敤甯舵湁鍏紡鍜屾枃鏈瓨鍎插姛鑳界殑瑷堢畻鍣�銆�
涓�銆佽│鍗峰収(n猫i)瀹硅垏椤屽瀷绲愭
濉┖(6 鍊嬬┖ 锛屾瘡绌� 5 鍒�锛屽叡 30 鍒�)
瑷堢畻椤�(4 灏忛锛屾瘡椤� 10 鍒�锛� 鍏� 40 鍒�)
璀夋槑椤�(4 灏忛锛屾瘡椤� 10 鍒嗭紝 鍏� 40 鍒�)
缍滃悎鎳夌敤椤�(40 鍒�)
鍋囧姣忛鍒嗘暩(sh霉)鏈夎畩鍖�锛岃畩鍖栬寖鍦嶄害涓嶅ぇ銆�
III 鑰冩煡鍏�(n猫i)瀹�
1. 闆嗗悎鐨勬蹇�銆侀亱绠�銆侀劙鍩熺殑瀹氱京锛涘嚱鏁�(sh霉)鐨勬蹇�銆佸湒褰€€佽〃绀烘硶锛涘熀鏈垵绛夊嚱鏁�(sh霉)锛氬啰鍑�
鏁�(sh霉)锛涙寚鏁�(sh霉)鍑芥暩(sh霉)锛涘皪鏁�(sh霉)鍑芥暩(sh霉)锛涗笁瑙掑嚱鏁�(sh霉)锛涘弽涓夎鍑芥暩(sh霉)锛涘弽鍑芥暩(sh霉); 寰╁悎鍑芥暩(sh霉)鐨勬蹇�; 鍒濈瓑鍑芥暩(sh霉); 闆�
鏇插嚱鏁�(sh霉)鍜屽弽闆欐洸鍑芥暩(sh霉)鐨勬蹇�; 鍑芥暩(sh霉)鐨勬湁鐣屾€�銆佸柈瑾�(di脿o)鎬с€佸鍋舵€�銆佸懆鏈熸€с€佸嚱鏁�(sh霉)妤甸檺锛堟暩(sh霉)鍒楁サ
闄愶級瀛樺湪鎬�銆佽▓绠�銆佺劇绐皬闅庣殑姣旇純锛涘嚱鏁�(sh霉)閫ｇ簩(x霉)鎬у強闁夊崁(q奴)闁撻€ｇ簩(x霉)鍑芥暩(sh霉)鎬ц唱銆�
2. 灏庢暩(sh霉)鐨勫畾缇�銆佸乏鍙冲皫鏁�(sh霉)銆佸皫鏁�(sh霉)鐨勭墿鐞嗘剰缇╁拰骞句綍鎰忕京锛涘嚱鏁�(sh霉)鐨勫彲灏庢€ц垏閫ｇ簩(x霉)鎬х殑闂滅郴锛�
灏庢暩(sh霉)鐨勫洓鍓囬亱绠楁硶鍓囥€佸弽鍑芥暩(sh霉)鐨勫皫鏁�(sh霉)銆佸京鍚堝嚱鏁�(sh霉)鐨勬眰灏庢硶鍓囷紱楂橀殠灏庢暩(sh霉)鐨勬蹇�銆侀珮闅庡皫鏁�(sh霉)鐨�
瑷堢畻鏂规硶銆佽悐甯冨凹鑼ㄥ叕寮�銆侀毐鍑芥暩(sh霉)姹傚皫娉曪紱灏嶆暩(sh霉)姹傚皫娉�锛涘弮鏁�(sh霉)鏂圭▼琛ㄧず鐨勫嚱鏁�(sh霉)鐨勫皫鏁�(sh霉)锛涚浉闂�
璁婂寲鐜�锛涘井鍒嗙殑瀹氱京; 鍑芥暩(sh霉)鍙井鐨勬浠讹紱鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勫井鍒嗗叕寮忚垏寰垎閬嬬畻娉曞墖锛涘井鍒嗙殑
骞句綍鎰忕京銆佸嚱鏁�(sh霉)鐨勭窔鎬у寲銆�
3. 缇呯埦瀹氱悊銆佹媺鏍兼湕鏃ヤ腑鍊煎畾鐞嗐€佹煰瑗夸腑鍊煎畾鐞�锛涙礇蹇呴仈娉曞墖銆佹嘲鍕掑叕寮�
鍑芥暩(sh霉)鐨勫柈瑾�(di脿o)鎬�銆佹洸绶氱殑鍑瑰嚫鎬с€佸嚱鏁�(sh霉)鐨勬サ鍊�銆佸嚱鏁�(sh霉)鍦栧舰鐨勬弿绻紱寮у井鍒嗙殑姒傚康銆佸井鍒嗕笁瑙掑舰銆�
鏇茬巼鍙婂叾瑷堢畻鍏紡銆佹洸鐜囧湏鐨勬蹇�锛涙眰杩戜技瀵︽牴浜屽垎娉曞拰鍒囩窔娉�(鐗涢爴娉�)銆�
3
4. 鍘熷嚱鏁�(sh霉)鐨勬蹇�銆佷笉瀹氱⿳鍒嗙殑姒傚康銆佷笉瀹氱⿳鍒嗙殑鎬ц唱锛涘熀鏈⿳鍒嗚〃锛涚洿鎺ョ⿳鍒嗘硶锛氱涓€
鎻涘厓绌嶅垎娉�(婀婂井鍒嗘硶)锛涘父鐢ㄦ箠寰垎鍏紡锛涚浜屾彌鍏冩硶锛涘垎閮ㄧ⿳鍒嗘硶锛涙湁鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒嗭紱鍙�
鍖栫偤鏈夌悊鍑芥暩(sh霉)鐨勭⿳鍒嗭細1锛庝笁瑙掑嚱鏁�(sh霉)鏈夌悊寮忕殑绌嶅垎锛�2锛庣啊鍠劇鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒�銆�
5. 瀹氱⿳鍒嗙殑姒傚康銆佸畾绌嶅垎鐨勮繎浼艰▓绠�锛涘畾绌嶅垎鍔犳硶娉曞墖銆佹暩(sh霉)涔樻硶鍓�銆佷笉绛夊紡鎬ц唱銆佸畾绌�
鍒嗕腑鍊煎畾鐞�銆佺墰闋撯€旇悐甯冨凹鑼插叕寮忥紱绌嶅垎涓婇檺鐨勫嚱鏁�(sh霉)鍙婂叾灏庢暩(sh霉)锛涘畾绌嶅垎鐨勬彌鍏冩硶绌嶅垎娉曞拰鍒�
閮ㄧ⿳鍒嗘硶锛涚劇绐檺鐨勫唬缇╃⿳鍒�銆佺劇鐣屽嚱鏁�(sh霉)鐨勫唬缇╃⿳鍒�锛涚劇绐檺寤ｇ京绌嶅垎鐨勫鏂傛硶銆佺劇鐣屽嚱鏁�(sh霉)
鐨勫唬缇╃⿳鍒嗗鏂傛硶銆� ?鍑芥暩(sh霉)瀹氱京鍙婂叾鎬ц唱銆�
6. 瀹氱⿳鍒嗙殑寰厓娉�銆佸钩闈㈠湒褰㈢殑闈㈢⿳銆佹棆杞夐珨鐨勯珨绌�銆佸钩琛屾埅闈㈤潰绌嶇偤宸茬煡鐨勭珛楂旂殑楂�
绌�銆佸钩闈㈡洸绶氬姬闀风殑姒傚康銆佸钩闈㈡洸绶氱殑寮ч暦鐨勮▓绠椼€佽畩鍔涙部鐩寸窔鎵€浣滅殑鍔�銆佹按澹撳姏銆佸紩鍔�銆�
7. 甯稿井鍒嗘柟绋嬬殑姒傚康銆佹柟绋嬬殑闅庢暩(sh霉)銆佺窔鎬у井鍒嗘柟绋�銆侀潪绶氭€у井鍒嗘柟绋嬶紱寰垎鏂圭▼鐨勮В锛堥€�
瑙�銆佺壒瑙ｏ級; 寰垎鏂圭▼鐨勭⿳鍒嗘洸绶氾紱鍙垎闆㈣畩閲忕殑寰垎鏂圭▼銆佸垎闆㈣畩閲忔硶銆侀綂娆℃柟绋�锛涗竴闅�
绶氭€у井鍒嗘柟绋�銆佸父鏁�(sh霉)璁婃槗娉�銆佷集鍔埄鏂圭▼锛涘彲闄嶉殠鐨勪簩闅庡井鍒嗘柟绋�锛涗簩闅庡父绯绘暩(sh霉)榻婃绶氭€у井
鍒嗘柟绋嬪強鍏惰В娉曪紱浜岄殠甯哥郴鏁�(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋�锛涙瓙鎷夋柟绋�锛涘父绯绘暩(sh霉)绶氭€у井鍒嗘柟绋嬬祫銆�
IV. 椤屽瀷绀轰緥鍙婂弮鑰冪瓟妗�
涓€. 濉┖椤岋紙姣忛 5 鍒�锛屽叡 30 鍒嗭級
1. 鍑芥暩(sh霉) 2
45
sin
)3lg(
)( xx
x
x
xf ???
?
? 鐨勫畾缇╁煙鐐篲____________.
2. 鐢辨柟绋� 1ln ?? yxy 鎵€纰哄畾鐨勫嚱鏁�(sh霉) )(xfy ? 鍦ㄩ粸 )1,1(M 铏曠殑鍒囩窔鏂圭▼________.
3. 瑷嚱鏁�(sh霉)
?
?
?
?
?
?
?
?
?
0,
0,
)2/arcsin(
1
)(
2
tan
xae
x
x
e
xf
x
x
鍦� 0?x 铏曢€ｇ簩(x霉)锛屽墖 ?a _______.
4. 瀹氱⿳鍒�??
?
1
1
2
)sin|(| dxxxx =__________.
5. ??
??
?
0
3
dxex
x
_______.
6. ?
?
?
?
?
?
?
3
2
1
x
t
dte
dx
d
=____________.
浜�.瑷堢畻椤�(姣忓皬椤� 10 鍒�锛屽叡 40 鍒�)
1. 姹� .
cossec
)1ln()1ln(
lim
22
0 xx
xxxx
x ?
?????
?
2. 瑷� )1(
)4(
1)1(
2
3
?
?
??
? x
ex
xx
y
x
, 姹� y ? .
3. 姹傜敱涓嬪垪鏂圭▼ )ln()(2 yxyxxy ???? 鎵€纰哄畾鐨勫嚱鏁�(sh霉) )(xyy ? 鐨勪簩闅庡皫鏁�(sh霉).
.
4. 宸茬煡 )( xf 鐨勪竴鍊嬪師鍑芥暩(sh霉)鏄�
2
x
e
?
, 姹�? ? dxxfx )( .
4
涓�.璀夋槑椤�(姣忛 10 鍒�,鍏� 40 鍒�)
1. 璀夋槑: 鍑芥暩(sh霉) 2
2 xxy ?? 婊胯冻闂滅郴寮� .01
3
????yy
2. 璀夋槑鏂圭▼
0
3
1
2
1
1
1
?
?
?
?
?
? xxx
鏈夊垎鍒ュ寘鍚簬(1, 2), (2, 3) 鍏�(n猫i)鐨勫叐鍊嬪鏍�.
3. 璀夋槑鐣� 0?x 鏅�, .)1ln(
1
xx
x
x
???
?
4. 鑻� )(xf 鍦╗0, 1]涓婇€ｇ簩(x霉), 璀夋槑
(1) ;)(cos)(sin
2/
0
2/
0 ?? ?
??
dxxfdxxf
(2) ,)(sin
2
)(sin
00 ?? ?
?? ?
dxxfdxxxf 鐢辨瑷堢畻 .
cos1
sin
0
2? ?
?
dx
x
xx
鍥�. 缍滃悎鎳夌敤椤�(姣忛 10 鍒�,鍏� 40 鍒�)
1. 瑷伐寤� A 鍒伴惖璺窔鐨勫瀭鐩磋窛闆㈢偤 20km, 鍨傝冻鐐� B. 閻佃矾绶氫笂璺濋洟 B 鐐� 100km 铏曟湁涓€鍘熸枡
渚涙噳绔� C, 濡傚湒 3-5-4. 鐝�(xi脿n)鍦ㄨ鍦ㄩ惖璺� BC 涓枔鏌愯檿 D 淇缓涓€鍊嬪師鏂欎腑杞夎粖绔�, 鍐嶇敱杌婄珯 D 鍚�
宸ュ粻淇竴姊濆叕璺�. 濡傛灉宸茬煡姣弅m 鐨勯惖璺亱璨昏垏鍏矾閬嬭不涔嬫瘮鐐�3:5, 閭ｄ箞, D鎳夐伕鍦ㄤ綍铏�, 鎵�
鑳戒娇鍘熸枡渚涙噳绔� C 閬嬭波鍒板伐寤� A 鎵€闇€閬嬭不鏈€鐪�?
2. 娌虫按浠� 绉掔背 /8
3
鐨勯珨娴侀噺娴佸叆姘村韩涓�, 姘村韩褰㈢媭鏄暦鐐� 4000 绫�, 闋傝鐐� ?120 鐨勬按妲�, 鍟�
姘存繁 20 绫虫檪, 姘撮潰姣忓皬鏅備笂鍗囧咕绫�?
姘存Ы姗埅闈㈠湒姘存Ы姗埅闈㈠湒
3. 鍦ㄤ竴鍊嬬煶娌圭簿鐓夊粻锛屼竴鍊嬪瓨鍎茬綈瑁� 8000L 鐨勬苯娌�锛屽叾涓寘鍚� 100g 鐨勬坊鍔犲姂. 鐐哄啲瀛ｆ簴鍌�锛�
姣忓崌鍚� 2g 娣诲姞鍔戠殑鐭虫补浠� 40L/min 鐨勯€熷害娉ㄥ叆瀛樺劜缃�. 鍏呭垎娣峰悎鐨勬憾娑蹭互 45L/min 鐨勯€熷害
娉靛嚭. 鍦ㄦ贩鍚堥亷绋嬮枊濮嬪悗 20 鍒嗛悩缃愪腑鐨勬坊鍔犲姂鏈夊灏�锛�
4. 鎸夌収浠ヤ笅姝ラ浣滃嚭鍑芥暩(sh霉) ?? 104
34
??? xxxf 鐨勫湒褰�.
(1) 姹� ? ?xf ? 鍜� ? ?xf ?? ;
(2) 鍒嗗垾姹� ? ?xf ? 鍜� ? ?xf ?? 鐨勯浂榛�;
(3) 纰哄畾鍑芥暩(sh霉)鐨勫娓涙€с€佸嚬鍑告€�銆佹サ鍊奸粸鍜屾嫄榛�;
5
(4) 浣滃嚭鍑芥暩(sh霉) ?? 104
34
??? xxxf 鐨勫湒褰�.
鍙冭€冪瓟妗�:
涓€銆佸～绌洪
1. ).3,0(}0,1[}0,3,3|{ ???????? xxxxDf
2. )1(
2
1
1 ???? xy 锛屽嵆 .032 ??? yx
3. 2
4.
2
1
.
5. 6.
6. ?
6
2
3
x
ex
浜�銆佽▓绠楅
1. 瑙� 鍏堢敤灏嶆暩(sh霉)鎬ц唱鍖栫啊鍒嗗瓙锛屽緱鍘熷紡 ,
cossec
)1ln(
lim
42
0 xx
xx
x ?
??
?
?
鍥犵偤鐣� 0?x 鏅傦紝鏈� ,~)1ln(
4242
xxxx ???
xx cossec?
x
x
cos
cos1
2
?
?
x
x
cos
sin
2
? .~
2
x 鎵€浠ュ師寮� 2
42
0
lim
x
xx
x
?
?
?
.1?
2. 瑙� 绛夊紡鍏╅倞鍙栧皪鏁�(sh霉)寰�
,)4ln(2)1ln(
3
1
)1ln(ln xxxxy ???????
涓婂紡鍏╅倞灏� x姹傚皫寰�
,1
4
2
)1(3
1
1
1'
?
?
?
?
?
?
?
xxxy
y
? .1
4
2
)1(3
1
1
1
)4(
1)1(
' 2
3
?
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xxxex
xx
y x
3. 瑙� ? ,
'1
)()ln()'1(2'
yx
y
yxyxyy
?
?
??????
?
)ln(2
1
1'
yx
y
??
??
6
?
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??
)ln(2
1
)''(''
yx
yy 2
)]ln(2[
])ln(2[
yx
yx
??
???
?? 2
)]ln(2)[(
1
yxyx
y
???
??
?? (浠ｅ叆 y ? )
.
)]ln(2)[(
1
3
yxyx ???
?
4. 瑙� ?? ?? )()( xxdfdxxfx
??? ,)()( dxxfxxf
鏍规摎(j霉)椤屾剰 ,)(
2
Cedxxf
x
??
?
? 鍐嶆敞鎰忓埌 ? ? ),()( xfdxxf ?
?
?
鍏╅倞鍚屾檪灏� x姹傚皫锛屽緱 ,2)(
2
x
xexf
?
??
?? ???? dxxfxxfdxxfx )()()( .2
22
2
Ceex
xx
????
??
涓夈€佽瓑鏄庨
1. 璀� 灏� 2
2 xxy ?? 姹傚皫锛屽緱
)2(
22
1 2
2
???
?
?? xx
xx
y ,
22
1
2
xx
x
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2
22
2
)2()1(2)1(
xx
xxxxxx
y
?
?????????
???
2
2
2
2
22
22
)1(2
xx
xx
x
xxx
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2)2(
)1(2
xxxx
xxx
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2/32
)2(
1
xx ?
?? .
1
3
y
??
浠ｅ叆鍘熸柟绋�,寰� .01
3
????yy 璀夌暍.
2. 璀� 鐣� ,3,2,1?x 鐢� )3)(2)(1( ??? xxx 涔樻柟绋嬪叐绔�锛屽緱
.0)2)(1()3)(1()3)(2( ????????? xxxxxx
瑷� ,)2)(1()3)(1()3)(2()( ????????? xxxxxxxf 鍓�
,02)2()1()1( ??????f ,01)1(1)2( ??????f ,0212)3( ????f
鐢遍浂榛炲畾鐞嗙煡锛� )( xf 鍦� )2,1( 鑸� )3,2( 鍏�(n猫i)鑷冲皯鍚勬湁涓€鍊嬮浂榛烇紝鍗冲師鏂圭▼鍦� )2,1( 鑸� )3,2( 鍏�(n猫i)
鑷冲皯鍚勬湁涓€鍊嬪鏍�.
3. 璀� 瑷� ),1ln()( xxf ?? 鍓� )( xf 鍦� ],0[ x 涓婃豢瓒虫媺鏍兼湕鏃ュ畾鐞嗙殑姊濅欢. 鏁�
)0)(()0()( ???? xffxf ? ),0( x???
? ,0)0( ?f ,
1
1
)(
x
xf
?
??
寰炶€�
??
??
1
)1ln(
x
x ),0( x???
鍙堢敱 x???? 111 ? ? ,1
1
1
1
1
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? ?x
? ,
11
x
x
x
x
?
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? ?
7
鍗� .)1ln(
1
xx
x
x
???
?
4. 璀� (1) 瑷� tx ??
2
?
? 0, ??? xdtdx ?
2
,
2
??
?? xt ? ,0?t
?
2
0
)(sin
?
dxxf
? ?
?
?
?
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0
2
2
sin?
?
dttf ?? 2
0
)(cos
?
dttf ;)(cos2
0??
?
dxxf
(2) 瑷� tx ?? ? ? 0, ??? xdtdx ? ?? ?? xt , ? ,0?t
?
?
0
)(sin dxxxf
? ????
0
)][sin()(
?
?? dttft ,)(sin)(
0? ??
?
? dttft
?? ??
??
?
00
)(sin)(sin dtttfdttf ,)(sin)(sin
00 ?? ??
??
? dxxxfdxxf
.)(sin
2
)(sin
00 ?? ??
?? ?
dxxfdxxxf
?? ?
?
?
?? ?
0 20 2
cos1
sin
2cos1
sin
dx
x
x
dx
x
xx
? ?
??
??
0 2
)(cos
cos1
1
2
xd
x
? ? .
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)arctan(cos
2
2
0
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?????? x
鍥�銆佺稖鍚堟噳鐢ㄩ
1. 瑙� 瑷� xBD? (km), 鍓� xCD ??100(km), .20
22
xAD ??
閻佃矾姣忓叕閲岄亱璨� ,3 k 鍏矾姣忓叕閲� ,5 k 瑷橀偅閲岀附閬嬭不鐐� y锛屽墖鏈夊涓嬪嚱鏁�(sh霉)闂滅郴寮�:
CDkADky ???? 35
鍗� ).1000()100(34005
2
??????? xxkxky
鍟忛姝哥祼鐐猴細 x鍙栦綍鍊兼檪鐩鍑芥暩(sh霉) y鏈€灏�.
姹傚皫寰� ,3
400
5
2 ?
?
?
?
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?
?
??
x
x
ky 浠� 0??y 寰� 15?x (km).
鐢变簬 .26100)100(,380)15(,400)0( kykyky ???
寰炶€岀暥 15?BD (km)鏅�锛岀附閬嬭不鏈€鐪�.
2. 瑙� 瑷� )(tV 琛ㄧず姘村韩鍦ㄦ檪鍒籺姘寸殑楂旂⿳, 鍓囨湁 ,34000)(
2
htV ?
涓婂紡鍏╅倞灏� t姹傚皫寰�
dt
dh
h
dt
dV
?? 38000
? 28800?
dt
dV
绫� 3
/灏忔檪,
8
?鐣� 20?h 绫虫檪, 104.0?
dt
dh
绫�/灏忔檪锛堟按闈笂鍗囦箣閫熺巼锛�銆�
3. 瑙� 浠� y鏄湪鏅傚埢 t缃愪腑鐨勬坊鍔犲姂鐨勭附閲�. 鏄撶煡 100)0( ?y . 鍦ㄦ檪鍒籺缃愪腑鐨勬憾娑茬殑
绺介噺
?? ? ? tttV 5800045408000 ?????
鍥犳锛屾坊鍔犲姂娴佸嚭鐨勯€熺巼鐐�
??
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t
ty
t
ty
tV
ty
58000
45
45
58000 ?
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娣诲姞鍔戞祦鍏ョ殑閫熺巼 80402 ?? 锛屽緱鍒板井鍒嗘柟绋�
t
y
dt
dy
58000
45
80
?
??
鍗�
80
58000
45
??
?
? y
tdt
dy
浜庢槸锛屾墍姹傞€氳В鐐�
? ? ? ?958000
45
58000
45
1600101600080 ????
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? tCtCdteey
dt
t
dt
t
鐢� 100)0( ?y 纰哄畾 C锛屽緱
? ? ? ? 01600001016000
9
????? C 锛� 8
1600
10
?C 锛�
鏁呭垵鍊煎晱椤岀殑瑙ｆ槸
? ? ? ?9
8
1600
1600
10
1016000 ???? tty 锛�
鎵€浠ユ敞鍏ラ枊濮嬪悗 20 鍒嗛悩鏅傜殑娣诲姞鍔戠附閲忔槸
? ? ? ? 58.1512160020
1600
10
201016000)20(
9
8
??????y g.
4. 瑙� (1) ?? 23
124 xxxf ??? 锛� ?? xxxf 2412
2
???? .
(2) 鐢� ?? 0124
23
???? xxxf 锛屽緱鍒� 0?x 鍜� 3?x .
鐢� ?? 02412
2
????? xxxf 锛屽緱鍒� 0?x 鍜� 2?x .
(3) 鍒楄〃纰哄畾鍑芥暩(sh霉)鍗囬檷鍗€(q奴)闁�銆佸嚬鍑稿崁(q奴)闁撳強妤靛€煎拰鎷愰粸锛�
x
? ?0,??
0
? ?2,0
2
? ?3,2
3
? ???,3
? ?xf ?
- 0 - 0 - 0 +
9
? ?xf ??
+ 0 - 0 + 0 +
? ?xf
鎷愰粸 鎷愰粸 妤靛€奸粸
(4) 绠楀嚭 0?x 锛� 2?x 锛� 3?x 铏曠殑鍑芥暩(sh霉)鍊�
? ? 100 ?f 锛� ? ? 62 ??f 锛� ? ? 173 ??f .
鏍规摎(j霉)浠ヤ笂绲愯珫锛岀敤骞虫粦鏇茬窔閫ｆ帴閫欎簺榛�锛屽氨鍙互鎻忕躬鍑�
鏁�(sh霉)鐨勫湒褰�.
5
1 0
1 5
?
?
?
5
1 0
1 5
? 1 1 2 3 4O x
y
鍏嶈铂鑱叉槑锛氭湰鏂囩郴杞夎級鑷恫(w菐ng)绲�锛屽鏈変镜鐘�锛岃珛鑱�(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€嬩汉瑙€榛�锛岃垏鏈恫(w菐ng)绔欑劇闂�銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹广€佹枃瀛楃殑鐪熷鎬�銆佸畬鏁存€�銆佸強鏅傛€ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰�锛屽苟璜嬭嚜琛屾牳瀵︾浉闂滃収(n猫i)瀹�銆�
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鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
