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5 Pages

Course: ECON 2965, Spring 2011
School: Fudan University
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Word Count: 973

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na 89501 a 1, a *4 2 n * 1P p&lt;0~ aa 2n 1 = a 2 a 15 *9 E 2 n 1 x aa a 2O 8 * ka 8 a = 2k + 1 a 2 2 a = 4k + 4k + 1 2 n 1 = 4k 2 + 4k + 1 8 2 n = 4k 2 + 4k + 2 2 n 1 = 2k 2 + 2k + 1 8 = xO * 8 , 2n 1 n 8 * 2 1O x n aa 2n 1 = a3 a 25 2 * 1 `#E aa a 3O X a2 a +1a 8 * 2 n = a 3 + 1 = (a + 1)(a 2 a + 1) a a 2 a + 1 a 2 n 8 8 8 8 8 a 8 2# 83 8 89502 * OX * 0 P &lt; p~ *4 a a OX a1 , a 2 , a 3...

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na 89501 a 1, a *4 2 n * 1P p<0~ aa 2n 1 = a 2 a 15 *9 E 2 n 1 x aa a 2O 8 * ka 8 a = 2k + 1 a 2 2 a = 4k + 4k + 1 2 n 1 = 4k 2 + 4k + 1 8 2 n = 4k 2 + 4k + 2 2 n 1 = 2k 2 + 2k + 1 8 = xO * 8 , 2n 1 n 8 * 2 1O x n aa 2n 1 = a3 a 25 2 * 1 `#E aa a 3O X a2 a +1a 8 * 2 n = a 3 + 1 = (a + 1)(a 2 a + 1) a a 2 a + 1 a 2 n 8 8 8 8 8 a 8 2# 83 8 89502 * OX * 0 P < p~ *4 a a OX a1 , a 2 , a 3 , , a n a k + a k +1 + a k + 2 + + a k + 6 < 0 8 k = 1 , 2 , 3 (1) a k + a k +1 + a k + 2 + + a k +10 > 0 8 k = 1 , 2 , 3 (2) a * nO * # 7 xE * n X O 11 8 2n 2 1 * 2 1O X n n , , 1E9 @ 7, * # E , @ 8 * 251 X O * # E * 5.54 X O 78%8 8 (1),(2) a k +7 + a k +8 + a k +9 + a k +10 > 0 8 * c8 e * c4 e (a) a8 + a9 + a10 + a11 > 0 (3) a11 + a12 + a13 + a14 > 0 (4) 8 (3)+(4) a8 + a9 + a10 + 2a11 + a12 + a13 + a14 > 0 a8 + a9 + a10 + a11 + a12 + a13 + a14 < 0 8 a12 > 0 a a13 > 0 a11 > 0 e c a11 + a12 + a13 > 0 a11 + a12 + a13 + a14 + a15 + a16 + a17 < 0 n 17 a 8 a14 + a15 + a16 + a17 < 0 8 (a)8 n < 17 e c 8 5,5,-13,5,5,5,-13,5,5,-13,5,5,-13,5,5,5,-13,5,5 , 8 16 8 na 8 Sn S17 8 b- 16 8 S1c 7 e a1 ~ a17 a S17 a 8 * a1 + a 2 + a3 + a 4 + a5 + a 6 + a 7 < 0 a 2 + a 3 + a 4 + a 5 + a 6 + a 7 + a8 < 0 a11 + a12 + a13 + a14 + a15 + a16 + a17 < 0 4 ce a 1. E * b * h 2. *ce * 3. ce 8 89503 + < c0 17 E @9 , @ ,7 8 4 f * f P < p * 8 *ce 8 8 * 14 ce n = 16 a 16 8 * 5.35 ce ce 76%8 8 8 c f 7, @E9 a, b, c 8 8 8 1, a, b, c (1 < a < b < c)P <*f4 2018 c+ < 0 4 1 + a < 1 + b < 1 + c a + b < a + c < b + c 1 + b < a + b 1 + c < a + c 1 + c 8 a + bc *E 8 18 1 + a < 1 + b < 1 + c < a + b < a + c < b + c (b + c) (a + c ) = + (a c) (a + b) = (a + b) (1 + c) = k (8 8 b a = c b = a + b c 1 = k b = a + k c = b + k = ( a + k ) + k = a + 2k a + ( a + k ) ( a + 2k ) 1 = k a = 2k + 1 a b = 3k + 1 a c = 4k + 1 8 *c'X 201 3(a + b + c + 1) = 201 a + b + c = 66 (2k + 1) + (3k + 1) + (4k + 1) = 66 k = 7 8 a = 15 a b = 22 a c = 29 a 28 1 + a < 1 + b < a + b < 1 + c < a + c < b + c a = 10 a b = 19 a c = 37 *cf c X' 1. 2.4 c+ < 0 a * 1.X c' c ' X* (c 2. 8 59%8 * 97 X c' a,b,c , c+ < 0 a,b,c a * 47 X c' 4.12 X c' 1+c a a+ b X' c 1+a<1+b<1+c a+b<a+c<b+c c' X 1+a<1+b<a+b<1+c<a+c<b+c a a,b,c a ) (8 51%)X c ' a,b,c*E c a,b,c p*f4 P< 1+c a a+b c (48%)8 89504 g w 8 *e 8 8 a,b,c 111 ++ abc (a 1)(b 1)(c 1) = abc (ab + bc + ca) + (a + b + c) 1 = (a + b + c) (ab + bc + ca) ab + bc + ca = (a + b + c) abc 111 = (a + b + c) ( + + ) > 0 abc a 1 , b 1 , c E* 1g h 8 a,b,c8 abc = 1 a w 18 g a 1 , b 1 , c 1 8 a,b,c 8 1 abc = 1 a a + b + c > 8 1. *e b)p 2. 8 8 e 8 8 8 *e 8 e 8 8 8 *e 8 e 8 * 131 e *e 8 3. e * 8 89505 8 8 e b)p 8 e 8e 8 e *e 8 8 *e * 4.88 e 8 *e 8 8 *e 8 88 8 *e 8 *e 88 88 *e 8 *e 8 88 8 8 88 8 70%8 8 8 8 8 * * f 4Pf 5 p < 58 68 7 8 *E b4 x ) 18 14 c+ < 0 c ' h na n3 H*E " " a,b8 1 8 50 h c' " c "h ' n = a + b + ab n = a + b + ab 8 n + 1 = ab + a + b + 1 = ( a + 1)(b + 1) 8 a,b n + 1 8 1 n 50 , 2 n + 1 51 8 8 2 8 51h* c' 15 8 8 n + 1c '* 4 , 9 , 25 , 49 8 a * , b' h n + 1 = ( a + 1)(b + 1) *c' c 8 1 8 * 50 c' 31 8 8 1. @ 7, 9 E @ 8 8 8 8 *c' h * 351 h c' *c' h 8 * 5.02 h c' 8 72%8 88 c' h 8 88 8 c' h c' h 8 8 8 8 2E . * - x 8 c' h 8 8* c ' h *c' h 3. c ' h 8 c' h * f * f P < p4 * f * f P < p4 89 8 E * 98 10 @ c
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Fudan University - ECON - 2965
a 89601 i *aE 20 Z3 \$+paE` i *aEA ,B,C*aE i 8 45 X* 55 840 8896028 x1 , x2 , x3 ,., x 7 8 * x1&lt;x2&lt;x3&lt;.&lt;x78 8 x1 + x2 + x3+.+x7=20008 x1+x2 + x 3 8 89603 ABC 8 AM . 8 8 BAC 8 * . ( AE A )AD A A BAC 848A8BMEDC89604 8 E Pe*, * * E Pe*, 88
Fudan University - ECON - 2965
89701 h D@8* 2000 x n 8 (n&gt;2)PC* * +89702 8 O*-ABC D h AO CBC = a, OA = a , AC = b, OB = b , AB = c, OC = c , a + a , b + b , c + c * +C*B89703 A 8 260 8 150 4 8 A 8 * D 45 h 8 45 n + u 0 e D8BCEF89704 8 nn h 8 n=3 n 3x * C 7@ 4 4=2 3 n 2=2
Fudan University - ECON - 2965
j 1 x0 8 89801 8 a , b , c * , d h a + b + c + d a+b = c ,b+c = d ,c+d = a8 * b h 889802 8 * a h x x + [ y ] + ( z ) = 1.5 y + [ z ] + ( x) = 7.7 z + [ x] + ( y ) = 2.6 [a ] H * a h (a ) ca [a ]c 89803 * H 0 @ + B n 3 H c 89804 0 * 0 h E I 8 C H
Fudan University - ECON - 2965
0 89901 8 89902 * 1| 89903 8 @ 7 E B@ C E @ 9 )7 x 2 ux 89904 ABCD cx 8 * ;O&amp; C * AOCD 1| * 1 ( | * 1| 8 89905 8 @ 9 )7 m E @ 9 )7 E @ 9 )7 * 1 | 4* uX 2E 8 (1)9 ) E @ 8 + 3 Y E H E52 8111111111111 1000000000005 + 1n + YE1 | *+=42 u * 2 E 1O |
Fudan University - ECON - 2965
0 891001(8 )8 *E 4 (1)@E9 7, * 2 (2) : *E E@8 8 8 8 8(8 )bt*f2 ( : *E )8 8 88 8 8 8 888 8 8889@8910028 E@ K*E 812 * 3 K*E 40 2 V+ u 4 K*E 5 K*E 60 8 12 * 891003 * n D E 7@ x , k 1 8 2 . 8 k . 8 * t n b2 k 891004 , * t b 2 (8 H * 1~n b2
Fudan University - ECON - 2965
111 8* 0 90110112 @ 7 E k901102*0@&lt; C,D x* (1)x (2)x / C,DE,F x* EFPx xx ODC x xxxCD P x &lt;C,D x* EFP EFP 0*iE 6CPDP CDAEOFBAEOFBBB901103 * 0@*&lt; kE @5 7O 9 kEf @5 7O 9 * 29 PiE 901104 G + + +* .+ G x1, x2, x3, ,x2001 x1= xk+1=
Fudan University - ECON - 2965
12 2K 6 * 0 901201(1)2 3 3 h* S B 2 1~9(h S B 2 K 2*yE (2)2 (1)h* S B 2 1~n (B Sh 2 6 E* 2 E y 9 )S B h* n n hS * B )B Sh* ( 6 *yE E K 6 (*yE 6H 2 *yE n 9 )2)2901202 B 2ABCD 2 2 AEF 22 ABD 2 2 ACD B S ABCD x L B42 12 BE B B ABD 2D E F A B C90
Fudan University - ECON - 2965
*E* 0 901301k Q *1000110000* k ,k = n, k Qn t,t ? Q110000901302 c . 7@E&quot;0 c . 7@E0 99 901303 * 9 17 Q EG @c 7. 0 Ej @c 7. 0 Q 9 901304 0 m * Q200 2 R+* 15m Q 52 R+* m E 4 9 901305 Q * 10 Q 9 * mE , * y ,k 3*2,99 (1)0 E) @c 7. 0 * ( 2)XE m
Fudan University - ECON - 2965
*)F* 0 901401*)F 9 *)F 20~1500 *pR3 B B1 *pR3 901402*F@+9014036 H|*)F @| 9 (1)X* Qa B*pR3 (2)X* Qa r p*)F Q 6 X* a 3 *F@+ B(*pR3 1~6 *pR3 B Q )X a5 *F@+901404 * XFF @ F (9 1234 94 321)H * 2088H 9 901405 C * _ ` F* ABCpR B *ABC 9AC B9 (
Fudan University - ECON - 2965
0 90150119 E H*i ! d ! *iEd H 8.99901502a=1+2+.+109 b=12+22+.+1029 c=13+23+.+103 9 d=14+24+.+104 9 1~10 9 * 2 S D a 1~10 9 * T + 9 S=1 2+1 3+1 4+.+8 10+9 109 T=1 2 3 4+1 2 3 5+1 2 3 6+.+6 8 9 10+7 8 9 109 9 a,b,c,d S9 T 949014034 4 1 4 4 9 4 4 2 4
Fudan University - ECON - 2965
*D* 0 901601 9 32000 9* 32001 ^ 9 901602 x4 0 9 ,9 * 0.5 4 D 9 1.5 9 , * ^37 9,x4 709 100 9 * =,H D , ^ 4 9 ,x4 1 9 ,99 901603 * ^ * 2001 @ 5 * 9 * 2001 ^A* 1 ^9 901604 * ^ ABCDE 9 1, 2, 3, 4, 59 9 9 12+ 34+ 5=_912 B E 53D C49 901605 @D&quot; 7
Fudan University - ECON - 2965
E Gv*/Gv*A0 3 p5 2 42 DBC901701* 9 cC `ABCD ` C c =39 =49 =59 ABCD 9P901702a1,a2,.,a2001 9 2001,2002,2003,.4000,4001 = * ^ E (1)(2001 1) (2002 2) (2003 3) . (4001 2001) a a a a Xb (2)(1 1) (2 2) (3 3) . (2001a2001) a a a cb 9017039C + c ` h
Fudan University - ECON - 2965
0 901801 X * (1) u (2) X] aX xx 12 3 + = 0x x a x+a ax xax 901802 9 n+1 X] 9 A,B,C C L 1, 5 , 5 2 , 5 3 , 5u n * * 2L 6 F A 4 n+1 99 901803 L C BH x DH u u a E9 F9 G9 H9 I9 J 9 DFJ * L 16 4 F A bx AB x AD x EF x BD x(1) a = b (2) a = b + 1 (3) a = b
Fudan University - ECON - 2965
*E* 0 901901100 ) q * 7 b @ G E 50 E * c E * q * ) q * ) x a b c 5 c x c a1 2 3 x 345* abc * x901902p cfw_ y x z x w cfw_* dq = 0.123 xyzw = 0.123xyzw23 xyzw23 xyzw 10 p pxq cfw_ dxx9019034k * + 1 y (1) 9 n d 1,5,9, *y ny an x a1 + a2 + a3 +
Fudan University - ECON - 2965
*@* 0 912001 * I Yx ^ p (k 0 2 9 * 6 2 1 * 48 k3 2@9 912002 ZI * 8 k 3 8 q * 8 q p q p a&lt;b * a,k b3 8 p, q 9 * a,k b3 8 , p* 0 0 k a,k b0 9 912003 CK @e &quot; 6 @GM*p@ @je * h |*4 (1) @U * I (2) 4 * * @I U* 83 k* 83 k912004 &quot; @e 1 1 @ @ 1 8 @ @ U I@
Fudan University - ECON - 2965
0 912101 u (1)9 n (2)9 n nff ( n) f * n n * i `- *9E f ( n) n * (N *9E f ( n)f ( 2307) = 2 + 3 + 0 + 7 = 12 ff 9121029 * 1 : * * N (9E 9 912103 *7 9 912104 )91 N 6(917 + B 24 9f 912105 9 * n : * nf180* n : * n 6 j( 8 i*9E )i*9E 9 (1)9 n = 7
Fudan University - ECON - 2965
0 912201 zC &lt; * M&lt; C z 2 2 2 (1) AH + BK +CP = H B 2+ KC 2 +PA2 (2) AH+BK+CP=HB+KC+PA ABC 9 MH,MK,MP9 9 H ,K,P &lt; z9 912202 * . E z = * . 1E 2 2912203 W1 9 W 2 9 W 3z C 9 &lt; W1 9 W 2 9 W 3 9 *z= N @ * A&lt; C z 829 359 21 9 zC &lt; W1 9 W 2 9 W 3 9 A9 B 9 C C
Fudan University - ECON - 2965
0 912301 9 9 ABCD AB + BM AD + DN AM = AN M9 N9 MAN=45099 912302 ABC E9 F 9 P9 / P: B c) =m9 =n9 / F: B = r9 m9 n9 a9 b9 c 9 EB : r 9 (9 = a 9 = b9 =D99 912303 (1)a9 b9 c9 d9 eR9 a+b9 c+d 9 b+c9 d+e 9 c+d9 e+a 9 d+e9 a+b 9 a9 b9 c9 d9 e(2)a9 b9 c9 d9
Fudan University - ECON - 2965
0 912401 (20021 )2 1 20022002 1 * (1 n1 =n (n1) (n2) 2 1 , n )1 912402 ( HH HH H H H * A B @+ F* ACB t 2 @ B A *C C 912403 1 2x2 11[x]+12=0 1 ([x] * x x=3.8[x]=31 x=-0.4[x]=-11 x=7[x]=7)1 912404A BCD= =10 ABC=100 0 1 CDA=130 0 1=9124058 7 6 5
Fudan University - ECON - 2965
E a * p * x 0 912501 h n n 4 * p8 K n n * p8 K1 912502 * 1 a @a E @ 7 E @a 1.a 2. * 3. &gt; * bd * a a E ac * 0h K 1912503 (1) A BCD A BCD &gt; * * x (2) A BCD A BCD &gt; * * x 2 U + ! x( 3 U + ! x(D F Cx 1) K hx 1) K hAE BB912504 *OH 24 * &gt;*4 *1H O (1)
Fudan University - ECON - 2965
*@* 0 912601 (1) (2) * x 2003200420052006+1 @ * ( 4567+1 , 9899100101+1)x * 912602 * x 1 1x * * l p * a ( @ M @ @ * @ 5 p @ * * l p * * l p * * l p ( ) an 1 bk 1 (1-bk)an 2003 a11 2 x a26 ) b11 b26 b20031 0 1 * 1 @ 2003 / a 2003( / *2003 / 0&lt; b1&lt;b2&lt;b20
Fudan University - ECON - 2965
0912701 1 1 t1, t2, t3, t4, t2003 1 t1=2 , tn+1 = , n=1,2,3,1 912702 1 1A 1 S1 M1,M2 1 300 1 (1 0 = = e1 H d D e )H D ( d e S H D S R9Ed 0 ) S S 1 912703 a,b He D a,b He D 7H de D 7H d e D M21d M2H eDM1K M1A V(1) (2)10a+b 5a+4ba-2b 4a-b7 79127
Fudan University - ECON - 2965
X2 920901 x C + Y E 1 2 382 * J Y * 2 920902 * x C F A *M o F A @ 7 F A @ 7 F A @ 7 * 7 M92 2 9 2(2 28 2 ) 212 22 38 50 2 26)1 + Y E * 9209 xCA F ( x C 121 2 3 4 * 5 6 x CA F 100100 * * J Y100100 1 + Y E 2 920903* 2M 1 7 F A @ * x F A 2M 2 7 F A
Fudan University - ECON - 2965
T 2 921001 + R 8 @ E ) + R 892 2 10 2(2 29 2 ) 21002 22DCAB2 9210021*d t * d t 22 38 * E 100 P ) 62 12 52 921003 @)E @ e @%V+p)E ) @ * d t 2 2 2 2 2 20 10 5 O * 3 t d 2 2 E *) 4 8 2 2 2 2 95 2 1 2 3 4 5 E) 02521021522022921004 1331 = 113
Fudan University - ECON - 2965
2 921101 A 2 + e 2 * p1x 92 2 11 2(2 30 2 ) 2100 &gt; 100 r @ E2 921102 * / &gt; E r *5 h8 gH * L20h8 * gH * L2 921103 2 X d2 p n * /8 ` E r d + e 72 2 * pn 22 9211042 x y y ( * / E rx + x 2 + x8 = y + y 2 + y 8x= y921105 2 ABC 6 / / 6 ABC y APBy B
Fudan University - ECON - 2965
921201 2 Q, N 2 H AM M ABC 2 BC H L 2 AB M AM M AC M P,AB AM AC , , u C AP AN AQAM 1 AB AC =( + )2 AN 2 AP AQ P B M NA2QCL2 921202 Ew 7@, 1 71 2 / , @ 7@E1 71 H * uC * 2 1X 7 * 2 2X 7 @ @ EF @,@ 5C @ E @,2 921203 uC AB 2 Em @, 7@ 1 * 7X 1P 56 2
Fudan University - ECON - 2965
&gt; 3 930201 * (1) * * * 393 3 2 3(3 32 3 ) 31,2,3,4 8 4,3,2,18 1 2 3 43 * ( 2) * * E *1 1r X 1 2 3 1,2,3,4,5,6 6,54,3,2,1X * 1r 4 5 63 * 1r X * E1. *1 2. F@993 930202 Fe 9 @D 2 * E *1 *1r X 7@13471897639233 13 121 3 2 &gt; * 122 X 1r 13 * 1 2X r930
Fudan University - ECON - 2965
393 3 3 3(3 33 3 )3933301 (1) 3 ` F p * Z d ^ T * W ( (2) 3 L F @ 7 ( G13 34 @ 7 F 23 G23 3n @ F n) G13G2933302m w* (1) (2) (3) (4) F@33 3 3m3 n *F n m3 n m3 nn w* (3)2x( 933303 3w p ABCD Phz0* *M PAB3 PBC3 PCD3 PDA F * (3P3933304 * M
Fudan University - ECON - 2965
y3 933401 + V u 1 3* 13K F 7 3* 23K F 7 93 3 4 3(3 34 3 ) 33 933402 3 3 2( 1( 1+2+-+108 * w 1 + 2 + L + 20 8 * 12 + 2 2 + + 10 2 13 + 2 3 + + 20 3933403 3 BD H w 3 C3 AB 3 P 3 CD H w D3 * AB H w PA A CE A E3 F H w Q3 PB A CF A AD3 R3QR / ABCP Q R
Fudan University - ECON - 2965
93 3 5 33 933501 3* N p * @ *j * p * @ * 10 fXI E 2(3 35 3 )3* 10 j * 10 j 10 j 10 3103 933502 3 M3 O3P QQQA BA3 B * Q M P Q 3 C3 D 3 3 A3 B3 * C3 D 3 O P C D MQ3 933503 * 3 3 3* abcde * 13 f W 23 33 3 bcJ K @ E * * f W E IaJ K @ E de33 93
Fudan University - ECON - 2965
3601(1)* C (2)1 3602 @ 8@cfw_E'X*p 1 5* S 3603 1 1 360411111 1PQRS S *yE EFGH 1 PQRS 1ABCD1 E1 F1 G1 H 1AP, BQ, CR, DS 11111 1 1 1 1 1 1 a = 1 + + + + + + + 1 b= S 2345 2003 2004 2005 1003 1004 2005 c = 1+ 3605 S EI P*yE 100 100 @cfw_E) 7H 31 201 11
Fudan University - ECON - 2965
*8=9 &quot;H3701 1A = cfw_ 2, 1,0,1,2,3 , B = cfw_ 1,2,3, 4,5 f :A B x + f ( x) + xf ( x) = 2k + 1, k f ( x) = 1, 2,3, 4,5 H E N *y x B 2, 1,0,1, 2,3 * 8 C* f 8C 3702 1 B 187 3703 1 x+ y =4 2 2 3 3 ( x + y )( x + y ) = 280 3704 5 K 5 AC B P 5 AK C * BP B
Fudan University - ECON - 2965
0u*=A3801GT F29 , 37 , 52 hB3802G cfw_G 10,G 9,G 8, 1,1,2,3,8,9,10A R+ R+A 1,nE@ 3803cfw_G n,G (n-1),G (n-2),1,1,2,3,n- c ( b10 F @ 71 a e d hj iabcd efg3804 E * E (1) . (2) 3805AE@ . 2GHG G G DF ACG G GG ABC * c FE G CE EG = FD FGFBC G
Fudan University - ECON - 2965
8 K p*7 d3901 * 1 pK*7 d85 55!@7 K 4 p*7 d3902 1380 9 AD 9 A I 9 AD 9 BIC9 90o9 1 BAC9 2I 9 ABC 93903 2380 9 90 @ 9 : aX* a,b,c a,b,c9 bH*7F c93904 3238 1. 9 2.: X 9 3.: X* : ,a / );a / , :,X* 15 9 (9 ) (a / 69 (9 ) ,9 ,9 ,9 ,9 ,94. @5 A * 5.A *
Fudan University - ECON - 2965
4001 21 1 @DO#+p 4002 8011 1 A 90o1 4003 ABC A MA MABA MBCA MCAA ) ) M * n v*D 5 *D v1 11 520055 4010 + 35 4010 114010 + 77 40104004@ @D'#+p @DK 78 ( 1)e *C7 ( 2)[ ; ; [ 4005AA B[ ;C(D [ ;ABCD A1 S1 1 [S]11+11 1 1 1 1 1 1 + 2 + 1+ 2 + 2 + 1+
Fudan University - ECON - 2965
+ (*, 4101C207B1 15ABCD A A AB =150 AD =240 BC =70 CD =200 ABD + BDC = 9000 0 ABCD 8 JD410224 2AA 20 + ! U 7 F @m(1m2005)w 20 8* J41030 x,y 8J 4104100 0,0 B0 cfw_(x,y)7 | x20 y20B0 a , b, c A111 1 += ,0 a b c a+b+c: 0 nA,1 a2 n +1+
Fudan University - ECON - 2965
4201 ABCD B ABD = 50o DBC = 20o DAC = 10o CAB = 40o ACD =DCA4202 H * * p M ; 1 1003 H AH B2005 B 1 B 2005 1H B B 4203 1. M C U H H N 1003 1B AA DY T GE H O B (B )S X DW O YE V O B (B )L E UB (B )B (B )X @+p)@AF * * p 1M ; F )@A9U \ A
University of Illinois, Urbana Champaign - CS - 105
FinalCS105Spring 2010May 7th, 2010DO NOT START UNTIL INSTRUCTED TO DO SO. YOU WILL LOSE POINTS IF YOU START WORKING ON THE TEST BEFORE WE TELL YOU. THIS IS A 150 MINUTE EXAM.Do not leave this blankfill it in now:Name: Discussion Section: TA:FORMA
University of Illinois, Urbana Champaign - CEE - 105
rF 1 ( 3)( O,O C ( t-,TFfrrfTF ( Z S O ( .1,'1' r i., , ,I II tr - r.r + g . . , -'r ; r . r'r rri s lDE2 f G 7 3 . !;.i '; c .i( i',rr'r r2 e eC@ .2 6 r '1-,r-.rr ' ' ' C :1i;7 4 t i.t'-z': 5 0 , A.)l.r?)'2-'t,;.'r'r'r t !)ig,-rf. r. ,'l 3 @ )ag)
University of Illinois, Urbana Champaign - CEE - 105
Midterm 1CS105Fall 2010September 28th, 2010DO NOT START UNTIL INSTRUCTED TO DO SO. YOU WILL LOSE POINTS IF YOU START WORKING ON THE TEST BEFORE WE TELL YOU. THIS IS A 60 MINUTE EXAM.Do not leave this blankfill it in now:Name: Discussion Section: TA:
University of Illinois, Urbana Champaign - CEE - 105
Midterm 2CS105Fall 2010November 2nd, 2010DO NOT START UNTIL INSTRUCTED TO DO SO. YOU WILL LOSE POINTS IF YOU START WORKING ON THE TEST BEFORE WE TELL YOU. THIS IS A 60 MINUTE EXAM.Do not leave this blankfill it in now:Name: Discussion Section: TA:F
University of Illinois, Urbana Champaign - CEE - 105
University of Illinois, Urbana Champaign - CEE - 105
Midterm 1CS105Spring 2010February 23rd, 2010DO NOT START UNTIL INSTRUCTED TO DO SO. YOU WILL LOSE POINTS IF YOU START WORKING ON THE TEST BEFORE WE TELL YOU. THIS IS A 60 MINUTE EXAM.Do not leave this blankfill it in now:Name: Discussion Section: TA
University of Illinois, Urbana Champaign - CEE - 105
Midterm 2CS105Spring 2010April 6th, 2010DO NOT START UNTIL INSTRUCTED TO DO SO. YOU WILL LOSE POINTS IF YOU START WORKING ON THE TEST BEFORE WE TELL YOU. THIS IS A 60 MINUTE EXAM.Do not leave this blankfill it in now:Name: Discussion Section: TA:FO
University of Illinois, Urbana Champaign - CEE - 105
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University of Illinois, Urbana Champaign - CEE - 105
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University of Illinois, Urbana Champaign - CEE - 105
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University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 1 2PM V1 September 25, 2008 50 points possibleName: Section Registered In:1. No hats or dark sunglasses. All hats are to be removed. 2. All book bags are to be closed and placed in a way that makes them inaccessible. Do not reach into your
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 2 2PM V1 October 16, 2009 50 points possibleName: Section Registered In:1. No hats or dark sunglasses. All hats are to be removed. 2. All book bags are to be closed and placed in a way that makes them inaccessible. Do not reach into your b
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 3 2PM V1 November 13, 2009 50 points possibleName: Section Registered In:1. No hats or dark sunglasses. All hats are to be removed. 2. All book bags are to be closed and placed in a way that makes them inaccessible. Do not reach into your
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 4 2PM V1 December 7, 2009 50 points possibleName: Section Registered In:1. No hats or dark sunglasses. All hats are to be removed. 2. All book bags are to be closed and placed in a way that makes them inaccessible. Do not reach into your b
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 2 2PM V1 October 20, 2008 55 points possible 1. Let F (x, y, z ) = (x + ez + y, yx2 ). (a) Find the best linear approximation of f (x, y, z ) at x = (1, 1, 0). (b) Explain what we mean when we say that the linearization in part (a) is the be
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 4 2PM V1 December 8, 2008 55 points possibleName: Section Registered In:1. Consider a metal wire in the shape of the parabola y = x2 , 1 x 3. (a) (3pts) Find a parametrization of the wire. y g/cm. Assumx ing that the units on the x-axis ar
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 3 9AM V1 November 16, 2008 55 points possible1. Let f : Rn R.Name: Section Registered In:(a) (3pts) State the formula for the second-order Taylor polynomial of f at the point a in Rn . (b) (2pts) In order for this expansion to be valid, w
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 1 Version 1 September 26, 2007 50 points possible 1. Consider the points A(5, 4, 7) and B (3, 0, 1). (a) (3pts) Find a vector equation or a set of parametric equations that denes the line containing points A and B . (b) (2pts) Determine if t
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 2 Version 1 1. (5pts) Find the domain and range of the function f (x, y ) = x . y2. (a) (4pts) Dene what it means a function f : Rn R to be continuous at x = a. for 2 3 3x y y if (x, y ) = (0, 0) is continuous at the origin. (b) (6pts) Show
University of Illinois, Urbana Champaign - MATH - 241
Math 241 Exam 3 Version 1 1. (5pts) Determine if the following statement is true or false. You do not need to justify your answer. For each part, you will receive 1 point for a correct answer, 1 point for an incorrect answer, and 0 points for no answer. E
University of Illinois, Urbana Champaign - MATH - 380
Name:Math 125 Exam 1 June 26, 2007 50 points possible1. (a) (3pts) Clearly state the Cauchy-Schwarz Inequality (b) (2pts) Dene the angle between the vectors a and b in Rn . (c) (2pts) Explain why Cauchy-Schwarz is necessary to dene angles in Rn when n &gt;
University of Illinois, Urbana Champaign - MATH - 380
Name:Math 380 Exam 2 July 16, 2007 50 points possible yz 2xz xy , , . 2 + z 2 x2 + y 2 + z 2 x2 + y 2 + z 2 +y (a) (4pts) Compute the divergence of F . x21. Let F (x, y, z ) =(b) (2pts) Interpret the divergence of F physically (or geometrically).2. (a
University of Illinois, Urbana Champaign - MATH - 380
Name:Math 380 Exam 3 August 1, 2007 50 points possible 1. If the density of a wire that lies along the planar curve (t) = (3t, t4 ), 0 t 1, is given by the function f (x, y ) = xy , nd the total mass of the wire.2. Let D be a region appropriate for Gree
University of Illinois, Urbana Champaign - MATH - 380
Name:Math 380 Exam 1 June 26, 2008 50 points possible 3 2 0 1. Let T (x) : R3 R3 be dened by the matrix A = 1 3 2 and let S (y) : R3 R 105 be dened by the matrix B = 4 0 2 (a) (1pt) Is S a vector-valued function? Briey explain your answer. (b) (2pts) Fin