các dạng bài tập toán cao cấp 1

Ngày tải lên: 05/07/2014, 10:55

Ngày tải lên: 05/03/2014, 10:20

Ngày tải lên: 24/09/2014, 22:31

Ngày tải lên: 17/11/2014, 08:22

... ∫ − −− = − −= 1 1 ln 2 1 1 1 1 1 2 1 )1) (1( 1 1 1 11 1 2 2 2 2 x x xxC sin1 sin1 ln 2 1 sin)( 2 − + −=⇒ Vậy ⇒No riêng : x x x x x xx xxy xxCxxCy R R sin1 sin1 lncos 2 1 ) sin1 sin1 ln 2 1 (sincos cossin cos)(sin)( 21 − + −= − + −+ −=⇒ += Như ...                                 = =        − = =        = − =        − = − = ⇔                    = − =       = − = ⇔      =− =− ⇔    = = 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 013 013 0' 0' 2 2 y x y x y x y x y y x x y x z z y x ⇒h/số có 4 điểm tới hạn: ) 3 1 , 3 1 ( 4 ), 3 1 , 3 1 ( 3 ) 3 1 , 3 1 ( 2 ), 3 1 , 3 1 ( 1 MM MM − −−− Ta ... )1( 1 2 C 1 C1 )o( y x3 e 2 x x e 2 C x3 e 1 Cy =+⇒= ++= )2(9 2 1 2 C 1 C39 )o( 'y x3 xe 2 3 x3 e 2 1 x e 2 C x3 e 1 C3'y =++⇒= ++ +=⇒ -Giải hệ [ ] xxx xeeey CC CC CC CC 33 12 11 21 21 211 15 4 1 4 11 4 15 11 4 15 2 15 2 )2( 2 17 3 )1( 1 +−= ⇒−=−=−= =⇒=⇒      =+ =+ 37 1/ 2 1 2 x Miền lấy t/phân D =           ≤≤− ≤≥ ∈ xyxx x Ryx 2 2 2 20 : 2 ),( ...

Ngày tải lên: 15/08/2012, 09:02

... z 1 , z 1 v`a z 2 (h˜ay v˜e h`ınh). 1. 1. D - i . nh ngh˜ıa sˆo ´ ph´u . c 7 (a 1 ,b 1 )+(a 2 ,b 2 ) def =(a 1 + a 2 ,b 1 + b 2 ). 1 (III) Ph´ep nhˆan (a 1 ,b 1 )(a 2 ,b 2 ) def =(a 1 a 2 − b 1 b 2 ,a 1 b 2 + ... d ´o P (z)=a 0 z n + a 1 z n 1 + ···+ a n 1 z + a n = a 0 z n + a 1 z n 1 + ···+ a n 1 z + a n = a 0 (z) n + a 1 (z) n 1 + ···+ a n 1 z + a n = a 0 (z) n + a 1 (z) n 1 + ···+ a n 1 z + a n = P (z). T`u . d ´oc˜ung ... ta c´o: Σ =1+ az + a 2 z 2 + ···+ a n z n = a n +1 z n +1 − 1 az − 1 (nhˆan tu . ’ sˆo ´ v`a mˆa ˜ usˆo ´ v´o . i a z − 1) = a n+2 z n − a n +1 z n +1 − a 2 +1 a 2 − a  z + 1 z  +1 (do z + 1 z = 2...

Ngày tải lên: 12/09/2012, 14:16

... nhiˆe ` ubiˆe ´ n 10 9 9 .1 D - a . oh`amriˆeng 11 0 9 .1. 1 D - a . o h`am riˆeng cˆa ´ p1 11 0 9 .1. 2 D - a . o h`am cu ’ a h`am ho . . p 11 1 9 .1. 3 H`am kha ’ vi 11 1 9 .1. 4 D - a . o h`am theo hu . ´o . ng 11 2 9 .1. 5 ... 1) 8. lim x 1  a 1 − x a − b 1 − x b  ; a, b ∈ N (D S. a − b 2 ) 9. lim x 1 (x n − 1) (x n 1 − 1) ···(x n−k +1 − 1) (x − 1) (x 2 − 1) ···(x k − 1) (D S. C k n ) 10 . lim x→a (x n − a n ) − na n 1 (x ... =    cos(n +1) 3 n +1 + ···+ cos(n + p) 3 n+p     1 3 n +1 + ···+ 1 3 n+p = 1 3 n +1 1 − 1 3 p 1 − 1 3 < 1 2 · 1 3 n < 1 3 n · Gia ’ su . ’ ε l`a sˆo ´ du . o . ng t`uy ´y. V`ı lim n→∞ 1 3 n =...

Ngày tải lên: 12/09/2012, 14:16

... +1 x− 1 ) 11 .  dx 3  (x +1) 2 (x− 1) 4 .(DS. 3 2 3  1+ x x − 1 ) 12 .  dx 4  (x − 1) 3 (x +2) 5 .(DS. 4 3 4  x − 1 x +2 ) 13 .  dx 3  (x − 1) 7 (x +1) 2 .(DS. 3 16 3x − 5 x − 1 3  x +1 x− ... . 16 2 12 .4.4 Cˆong th´u . cStokes 16 2 13 L´y thuyˆe ´ t chuˆo ˜ i 17 7 13 .1 Chuˆo ˜ isˆo ´ du . o . ng 17 8 13 .1. 1 C´ac d i . nh ngh˜ıa co . ba ’ n 17 8 13 .1. 2 Chuˆo ˜ isˆo ´ du . o . ng 17 9 13 .2 ... − 1 ) 3.   1 − x 1+ x dx x . (D S. 1 − √ 1 − x 2 x − arc sin x) 4.  3  x +1 x− 1 dx x +1 . (D S. − 1 2 ln (1 − t) 2 1+ t + t 2 + √ 3arctg 2t +1 √ 3 ,t= 3  x +1 x − 1 ) 5.  √ x +1 √ x− 1 √ x...

Ngày tải lên: 12/09/2012, 14:16

... nhiˆe ` ubiˆe ´ n 10 9 9 .1 D - a . oh`amriˆeng 11 0 9 .1. 1 D - a . o h`am riˆeng cˆa ´ p1 11 0 9 .1. 2 D - a . o h`am cu ’ a h`am ho . . p 11 1 9 .1. 3 H`am kha ’ vi 11 1 9 .1. 4 D - a . o h`am theo hu . ´o . ng 11 2 9 .1. 5 ... bi . ch˘a . n trˆen. Thˆa . tvˆa . y: a n = 1 5 +1 + 1 5 2 +1 + 1 5 3 +1 + ···+ 1 5 n +1 < 1 5 + 1 5 2 + ···+ 1 5 n = 1 5 − 1 5 n +1 1 − 1 5 = 1 4  1 − 1 5 n  < 1 4 · Nhu . vˆa . y d˜ay a n d˜achodo . nd iˆe . u ... 1) 16 . a n = n − 3 √ n 3 − n 2 .(DS. 1 3 ) 17 . a n = 1 − 2+3− 4+5−···−2n √ n 2 +1+ √ 4n 2 +1 .(D S. − 1 3 ) 18 . a n = 1 1 · 2 + 1 2 · 3 + ···+ 1 n(n +1) . Chı ’ dˆa ˜ n. ´ Ap du . ng 1 n(n +1) = 1 n − 1 n...

Ngày tải lên: 12/09/2012, 16:20

... nhiˆe ` ubiˆe ´ n 10 9 9 .1 D - a . oh`amriˆeng 11 0 9 .1. 1 D - a . o h`am riˆeng cˆa ´ p1 11 0 9 .1. 2 D - a . o h`am cu ’ a h`am ho . . p 11 1 9 .1. 3 H`am kha ’ vi 11 1 9 .1. 4 D - a . o h`am theo hu . ´o . ng 11 2 9 .1. 5 ... bi . ch˘a . n trˆen. Thˆa . tvˆa . y: a n = 1 5 +1 + 1 5 2 +1 + 1 5 3 +1 + ···+ 1 5 n +1 < 1 5 + 1 5 2 + ···+ 1 5 n = 1 5 − 1 5 n +1 1 − 1 5 = 1 4  1 − 1 5 n  < 1 4 · Nhu . vˆa . y d˜ay a n d˜achodo . nd iˆe . u ... ε>0 (lˆa ´ y ε = 1 2 ) ta c´o |a n − a| < 1 2 ∀ n  N. V`ı a n = ±1nˆen |1 − a| < 1 2 , | 1 − a| < 1 2 ⇒2=| (1 − a)+ (1+ a)|  |1 − a| + |a +1|  1 2 + 1 2 =1 ⇒2 < 1, vˆo l´y. 3) Lu . u´yr˘a ` ng...

Ngày tải lên: 12/09/2012, 16:20

... < 1 v ´ ’ oi n 0 ¯d ’ u l ´ ’ on. L ´ ˆay x = e n 0 +1 th`ı (P n 0 − I)e n 0 +1  ≤ P n 0 − I.e n 1 +1  < 1. M ˘ a . t kh´ac, ta c´o (P n 0 − I)e n 0 +1  = P n 0 e n 0 +1 − e n 0 +1  ... L{e 1 , . . . , e n }. V`ı {e n } l`a mˆo . t c ’ o s ’ ’ o c ’ ua X nˆen v ´ ’ oi mo . i x ∈ X ta c´o x = ∞  n =1 x, e n e n . Khi ¯d´o lim n→∞ P n x = lim n→∞ n  k =1 x, e k e k = ∞  n =1 x, ... c´o (P n 0 − I)e n 0 +1  = P n 0 e n 0 +1 − e n 0 +1  = e n 0 +1  = 1 (vˆo l´y) . 1 Ch ’ u ’ ong 2. Khˆong gian ¯di . nh chu ’ ˆan 10 . Cho A, B l`a hai to´an t ’ ’ u t´ıch phˆan trong C [a,b] v ´ ’ oi...

Ngày tải lên: 12/09/2012, 16:20

... a n =1 1 3 + 1 9 − 1 27 + ···+ ( 1) n 1 3 n 1 .(DS. 3 4 ) 20. a n = 2 n +1 +3 n +1 2 n +3 n .(DS. 3) 21. a n = n +( 1) n n − ( 1) n .(DS. 1) 22. a n =  1 √ n  1 √ 1+ √ 3 + 1 √ 3+ √ 5 + ···+ 1 √ 2n − 1+ √ 2n ... Tru . ´o . chˆe ´ ttach´u . ng minh r˘a ` ng 1 n(n + 1) (n +2) = 1 2  1 n(n +1) − 1 (n + 1) (n +2)  (D S. 1 4 ) 24. a n = 1 a 1 a 2 + 1 a 2 a 3 + ···+ 1 a n a n +1 .(DS. 1 a 1 d ) trong d ´o {a n } l`a cˆa ´ psˆo ´ cˆo . ng ... =    cos(n +1) 3 n +1 + ···+ cos(n + p) 3 n+p     1 3 n +1 + ···+ 1 3 n+p = 1 3 n +1 1 − 1 3 p 1 − 1 3 < 1 2 · 1 3 n < 1 3 n · Gia ’ su . ’ ε l`a sˆo ´ du . o . ng t`uy ´y. V`ı lim n→∞ 1 3 n =...

Ngày tải lên: 04/10/2012, 09:35

... Nˆe ´ u ε k 1  =1, t´u . cl`a k khˆong chia hˆe ´ tchon th`ı S = β k 0 1 − ε nk 1 1 − ε k 1 = β k 0 1 − 1 1 − ε k 1 =0 (v`ıε n 1 =1) . 24 Chu . o . ng 1. Sˆo ´ ph´u . c e 1+ i = e(cos 1 + i sin 1) , e πi/2 = ... c´o: 1/ nˆe ´ u z 1 = r 1 e iϕ 1 , z 2 = r 2 e iϕ 2 th`ı z 1 z 2 = r 1 r 2 e i(ϕ 1 +ϕ 2 ) , (1. 12) z 1 /z 2 = r 1 r 2 e i(ϕ 1 −ϕ 2 ) , (1. 13) 2/ nˆe ´ u z = re iϕ th`ı z n = r n e inϕ , (1. 14) n √ z ... chı ’ khi a 2 + b 2 − 1 (a +1) 2 + b 2 =0⇐⇒ a 2 + b 2 =1.  B ` AI T ˆ A . P T´ınh 1. (1 + i) 8 − 1 (1 − i) 8 +1 · (D S. 15 17 ) 2. (1+ 2i) 3 + (1 2i) 3 (2 − i) 2 − (2 + i) 2 · (DS. − 11 4 i) 3. (3 −...

Ngày tải lên: 26/10/2012, 15:44

... Ngũ                 − −− → →+− →               − − → → →+           − − − →+ → →           − − − → →+− →           − − 6 1 6 1 6 3 10 0 6 5 6 1 6 3 010 6 1 6 1 6 3 0 01 5 6 1 6 1 6 3 10 0 013 510 6 1 6 1 6 3 0 01 6 1 6 1 113 600 013 510 0 011 01 10 011 0 013 510 0 011 01 3 10 011 0 010 213 0 011 01 33 223 11 33 22 11 3 332 22 11 33 2 21 11 hh hhh hh hh hh hhh hhh hh hh hh hhh hh Ta ... có:             − − − −− → → → →             − − − −− ↔             − − − −− → → → →             − − − −− →+ →+ →+ →             −− −− − −− = 22 210 00 7 011 00 310 0330 712 011 7 011 00 22 210 00 310 0330 712 011 7 010 10 22 210 00 310 0330 712 1 01 7 010 10 310 0330 22 210 00 712 1 01 3 2 011 111 10 36033 803202 712 1 01 43 34 22 11 32 44 32 23 11 4 41 3 31 2 21 11 hh hh hh hh cc hh hh hh hh hhh hhh hhh hh A ⇒ r(A) ... có:           −−− −−−−− ++ →+ → →           +− −−−−− ++ ↔           +− −−−−− ++ →+− →++− →           ++ + ++ → → →           ++ ++ + = aaa aaaaa aa hhh hh hh aaaa aaaaa aa CC aaaa aaaaa aa hhh hh)h(a hh )(aa a aa hh hh hh )(aa aa a A 300 220 11 11 0 220 11 11 0 220 11 11 1 2 11 11 111 1 11 11 2 11 11 111 1 11 11 2 22 332 22 11 2 22 32 2 22 3 31 2 21 11 33 21 12 Biện luận:  Nếu )3()0(0)( −=∨=⇔=−−...

Ngày tải lên: 27/10/2012, 09:05

... = 1 −  1+ i 2  2 n  2 1 − 1+ i 2 = 1 −  1+ i 2  2 n +1 1 − 1+ i 2 · Ta cˆa ` n tnh 1+ i 2 2 n +1 = 1+ i 2 2 2 n = i 2 2 n = i 2 n 2 2 n = 1 2 2 n à Do d o = 1 1 2 2 n 1 1+ i 2 = 2 1 1 2 2 n 1 ... chı ’ khi a 2 + b 2 − 1 (a +1) 2 + b 2 =0⇐⇒ a 2 + b 2 =1.  B ` AI T ˆ A . P T´ınh 1. (1 + i) 8 − 1 (1 − i) 8 +1 · (D S. 15 17 ) 2. (1+ 2i) 3 + (1 2i) 3 (2 − i) 2 − (2 + i) 2 · (DS. − 11 4 i) 3. (3 − ... vuˆong l`a cˆa ´ psˆo ´ nhˆan. Nˆe ´ u ε k 1  =1, t´u . cl`a k khˆong chia hˆe ´ tchon th`ı S = β k 0 1 − ε nk 1 1 − ε k 1 = β k 0 1 − 1 1 − ε k 1 =0 (v`ıε n 1 =1) . ...

Ngày tải lên: 15/03/2013, 10:20

... d ´o P (z)=a 0 z n + a 1 z n 1 + ···+ a n 1 z + a n = a 0 z n + a 1 z n 1 + ···+ a n 1 z + a n = a 0 (z) n + a 1 (z) n 1 + ···+ a n 1 z + a n = a 0 (z) n + a 1 (z) n 1 + ···+ a n 1 z + a n = P (z). T`u . d ´oc˜ung ... chia: z 2 z 1 = a 1 a 2 + b 1 b 2 a 2 1 + b 2 1 + i a 1 b 2 − a 2 b 1 a 2 1 + b 2 1 · C ´ AC V ´ IDU . V´ı d u . 1. 1 + T´ınh i n .T`u . d ´och´u . ng minh r˘a ` ng a) i n + i n +1 + i n+2 + i n+3 =0; b) ... 1 (a +1) 2 + b 2 =0⇐⇒ a 2 + b 2 =1.  B ` AI T ˆ A . P T´ınh 1. (1 + i) 8 − 1 (1 − i) 8 +1 · (D S. 15 17 ) 2. (1+ 2i) 3 + (1 2i) 3 (2 − i) 2 − (2 + i) 2 · (DS. − 11 4 i) 3. (3 − 4i)(2 − i) 2+i − (3+4i)(2...

Ngày tải lên: 11/04/2013, 13:09

... d ˆo ’ ibiˆe ´ n (11 -14 ) 11 . lim x 1 x p q − 1 x r s − 1 (D S. ps qr ) 12 . lim x→ 1 1+ 3 √ x 1+ 5 √ x (D S. 5 3 ) 13 . lim x→0 3 3 √ 1+ x − 4 4 √ 1+ x +1 2 − 2 √ 1+ x + x (D S. 1 6 ) 14 . lim x→0 n √ 1+ x − 1 x (D S. 1 n ) Mˆo . t ... sˆo ´ 7. lim x 1  1 1 − x − 3 1 − x 3  (D S. 1) 8. lim x 1  a 1 − x a − b 1 − x b  ; a, b ∈ N (D S. a − b 2 ) 9. lim x 1 (x n − 1) (x n 1 − 1) ···(x n−k +1 − 1) (x − 1) (x 2 − 1) ···(x k − 1) (D S. ... 4+5−···−2n √ n 2 +1+ √ 4n 2 +1 .(D S. − 1 3 ) 18 . a n = 1 1 · 2 + 1 2 · 3 + ···+ 1 n(n +1) . Chı ’ dˆa ˜ n. ´ Ap du . ng 1 n(n +1) = 1 n − 1 n +1 (D S. 1) 7 .1. Gi´o . iha . ncu ’ a d˜ay sˆo ´ 25 7 .1. 4 Ch´u . ng minh...

Ngày tải lên: 11/04/2013, 13:09

... TOÁN CAO CẤP II 9. ( ) 4 4 0 , y dy f x y dx ∫ ∫ ĐS: ( ) 2 0 1 1 1 , x x dx f x y dy − − + ∫ ∫ 10 . ( ) 2 0 1 1 1 , x x dx f x y dy − − + ∫ ∫ ĐS: ( ) 2 1 1 0 1 , y y dy f x y dy − − − ∫ ∫ 11 . ( ... dy+ ∫ ∫ ∫ ∫ Bài 3: Tính các tích phân kép sau: 13 . ( ) 1 2 0 1 x x dx x y dy− + ∫ ∫ ĐS: 1 3 14 . 4 3 2 2 2 0 y y dy dx x y − + ∫ ∫ ĐS: 6 π 15 . ( ) 2 0 2 0 2 y dy x y dx+ ∫ ∫ ĐS: 11 ,2− 16 . 5 5 0 ... − ∫ ∫ 11 . ( ) 2 1 2 0 , x x dx f x y dy − ∫ ∫ ĐS: ( ) ( ) 2 1 2 0 0 1 0 , , y y dy f x y dx dy f x y dx − + ∫ ∫ ∫ ∫ 12 . ( ) 2 1 1 , y y dy f x y dx ∫ ∫ ĐS: ( ) ( ) 1 2 2 2 1 1 1 2 , , x x dx...

Ngày tải lên: 26/06/2013, 17:38

... !" # $% # &'()*  )  !0 10  )*+% #  '  .    % # &'()*  ). / '()*.'()*!(  +% #         −=+− =−+ =−− ⇔             xx xxx xxx 2  # )3  4  5+%  )&- # 63 7 3  73  4  5+%  )  ) α =  x !(  + α 4   10  -$  $   Nguyê ̃ n Phan Thanh Lâm MSV: 0 712 50 510 319 Trang 10 /20 Ba ̀ i tâ ̣ p toa ́ n cao cấp I GVHD: Phan Thi ̣ Ngu ̃          += −−= += ⇔          = −=+− =−+ =−− ⇔                 2        α α α α x x x x xx xxx xxx " # $% # &'()*  )  !0 10  )*+% #   )*+% # 0 8 )*9-  4         +−−+ αααα 6     6   6 !(  + α -$  $  2'        =−+−+ =−+− =+− =+−+−         xxxxx xxxx xxx xxxx                − − − −− → → → →             − − − −− ↔             − − − −− → → → →             − − − −− →+ →+ →+ →             −− −− − −− =                                    hh hh hh hh cc hh hh hh hh hhh hhh hhh hh A ⇒  ... !" # $% # &'()*  )  !0 10  )*+% #  '  .    % # &'()*  ). / '()*.'()*!(  +% #  Nguyê ̃ n Phan Thanh Lâm MSV: 0 712 50 510 319 Trang 11 /20 Ba ̀ i ... Ngu ̃ 3  4   )  )   4+ =         −+ → x Cosx x x π    ∞== == − =       −=       −=       − → →→ → → →→ tgx Cosx Sinx CosxSinx xSin CosxSinx xCos Sinx Cosx CosxSinx Sinx Cosx CosxSinx Cotx xSin x xx x x xx 4+ 4+4+ 4+ 4+ 4+4+                  π ππ π π ππ   '           ) 4+ 4+4+ 4+4+4+             == = − = − = − = − → →→ →→→ Cosx Cosxx x x Cosxx CosxSinx Cosxx CosxSinxSinx x Sinx Cosx Sinx x Sinxx x xx xxx   ;     4+4+  π πππ = − − = − →→ xSin x xCos xx Nguyê ̃ n Phan Thanh Lâm MSV: 0 712 50 510 319 Trang 15 /20 Ba ̀ i tâ ̣ p toa ́ n cao cấp I GVHD: Phan Thi ̣ Ngu ̃           − − − =−+=      AAAf 0           =−+=      BBBf     #   ) &  &  & 1  $           − − =    A 0           − =    B ($           −=    A 0           − −=    B *$           −−− − =    A 0           − −=    B 2           − − =    A 0           − =    B      − ∃⇒= AA ...

Ngày tải lên: 14/08/2013, 14:20

Ngày tải lên: 15/08/2013, 15:21