Bài tập toán cao cấp part 2 pdf

... hˆo.itu.1) an=n 2 − 1n 2 2) an =2+ 1 2! +13!+ ···+1n!Chı’dˆa˜n. T´ınh bi.ch˘a.ndu.o..csuyt`u.n!  2 n−1v`a do d´oan 2+ 1 2 +1 2 2+ ···+1 2 n−1=3−1 2 n−1< 3.4. ... c´o:an+1=√2an⇒ a 2 n+1=2an.Do d´o:lim a 2 n+1= 2 limanhay a 2 − 2a = 0 v`a thu du.o..c a1=0,a 2 =2. V`ı d˜ay do.ndiˆe.u t˘ang ∀n nˆen gi´o.iha.n a =2. V´ı du.4. ... an=1−13+19−1 27 + ···+(−1)n−13n−1.(DS.34) 20 . an= 2 n+1+3n+1 2 n+3n.(DS. 3) 21 . an=n +(−1)nn − (−1)n.(DS. 1) 22 . an=1√n1√1+√3+1√3+√5+ ···+1√2n − 1+√2n +1Chı’dˆa˜n....

Bài tập toán cao cấp part 9 pdf

... dw.Tac´o(6xy + w − 2) dx +(3x 2 +2yw 2 +1)dy +(3w 2 + x +2y 2 w)dw =0v`a do d´odw = 2 − 6xy − w3w 2 + x +2y 2 wdx −3x 2 +2yw 2 +13w 2 + x +2y 2 wdy. V´ı du.8. T´ınh dw v`a d 2 w cu’a h`am ... v`a d 2 w ta.idiˆe’m M(x, y) (19 -22 ) nˆe´u:19. w = f(lnz), z = x 2 + y 2 .(DS. d 2 w = 2 (x 2 + y 2 ) 2 (2x 2 ftt−x 2 ft+ y 2 ft)dx 2 +(4xyftt− 4xyft)dxdy +(x 2 ft− ... ydy)+4fvv(xdx + ydy) 2 +2ftdxdy +2fv(dx 2 + dy 2 ),d 2 uM0=2ft(0, 0)dxdy +2fv(0, 0)(dx 2 + dy 2 ),t = xy, v = x 2 + y 2 )T´ınh vi phˆan dnw (26 -27 ) nˆe´u: 26 . w = f(ax +...

Bài tập toán cao cấp - Phần 2 pptx

... + −∫ ∫=0( )( ) 2 2 2 211 114 1 1| 1 2 1 2 2 2 2yyJ x dy y dy y    = = − = − = − − − = ÷ ÷  ÷    ∫ ∫ 44 4 2 2 2 2 2 216 4| 2 2 8 4 1 2 4 4 4yy yK x ... 1 2 1 2 1tdtdtt t t t+ −⇔ =+ +∫ ∫ 2 21 1 1 1 1ln | | ln | 1| ln | | ln | 1| 2 1 2 2 2 2dt dtt t u ut t ⇔ − = − + = − + ÷+ ∫ ∫ (2) Thay (1) và (2) vào (***), có: 2 2 2 2 ... = 2, z = 0 và z = 2, tìm cận Ω.Giải: Từ hình vẽ ta có cận Ω= [0 ;2] x[0 ;2- x]x[0 ;2] ( ) 2 2 2 2 2 2 2 00 0 0 0 0 0( , , ) 2 2x xxI dx dy f x y z d z dydx y dx− −−= = =∫ ∫ ∫ ∫ ∫ ∫ 2 O 2 Dxyy...

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Bài tập toán cao cấp part 1 docx

... b)(a 2 − ab + b 2 )suy raan=3√n 2 − n3+ n3√n 2 − n3 2 − n3√n 2 − n3+ n 2 3√n 2 − n3 2 − n3√n 2 − n3+ n 2 =n 2 3√n 2 − n3 2 − n3√n 2 − n3+ n 2 =1[1/n ... gi´o.iha.ncu’a d˜ay: 0, 2; 0, 22 ; 0, 22 2; ,0, 22 2   n, Chı’dˆa˜n. Biˆe’udiˆe˜n andu.´o.ida.ngan=0, 22 2= 2 10+ 2 10 2 + ···+ 2 10n(DS. lim an =2/ 9)Mu.clu.c7 Gi´o.iha.n ... nˆen1+1 2 + ···+1 2 n= 2( 2n−1) 2 n,1+13+ ···+13n=3(3n−1) 2 · 3nv`a do d´o:lim an= lim 2( 2n−1) 2 n· 2 · 3n3(3n− 1)= 2 lim 2 n− 1 2 n· 2 3lim3n3n− 1= 2 lim[1...

Bài tập toán cao cấp part 3 ppsx

... (15 -26 )15. limx→0√1+x + x 2 − 1x(DS.1 2 )16. limx 2 √3+x + x 2 −√9 − 2x + x 2 x 2 − 3x +2 (DS.1 2 )17. limx→05x3√1+x −3√1 − x(DS.15 2 )18. limx→03√1+3x −3√1 − 2xx ... gi´o.iha.n sau dˆay(3-10).3. limx→72x 2 − 11x − 21 x 2 − 9x +14(DS.175)4. limx→1x4−x3+ x 2 − 3x +2 x3−x 2 − x +1(DS. 2) 5. limx→1x4+2x 2 −3x 2 −3x +2 (DS. −8)6. limx→1xm− 1xn− ... x)tgπx 2 (DS. 2 π)41. limx→11 − x 2 sin πx(DS. 2 π) 42. limx→πsin xπ 2 − x 2 (DS.1 2 )43. limx→0cos mx − cos nxx 2 (DS.1 2 (n 2 − m 2 ))44. limx→∞x 2 cos1x− cos3x(DS. 4)45....

Bài tập toán cao cấp part 4 pot

... nˆe´u:1. w =x 2 − y 2 .(DS. |y|  |x|) 2. w =√xy.(DS. x  0,y  0 ho˘a.c x  0,y  0)3. w =a 2 −x 2 − y 2 .(DS. x 2 + y 2  a 2 )4. w =1x 2 + y 2 − a 2 .(DS. x 2 + y 2 >a 2 )5. w ... x 2 + y 2 >a 2 )5. w =1 −x 2 a 2 −y 2 b 2 .(DS.x 2 a 2 +y 2 b 2  1)6. w = ln(z 2 − x 2 − y 2 − 1). (DS. x 2 + y 2 − z 2 < −1)7. w = arcsinx 2 +√xy.(DS. Hai nu.’a b˘ang vˆo ... limx→0y→31+xy 2 yx 2 y + xy 2 .(DS. e3)16. limx→0y→0x 2 yx 2 + y 2 .(DS. 0)17. limx→0y→5(x 2 +(y − 5) 2 +1− 1x 2 +(y − 5) 2 .(DS.1 2 )18. limx→1y→0tg(2xy)x 2 y.(DS. 2) .8.1....

Bài tập toán cao cấp part 5 ppt

... e−x 2 .(DS. 2e−x 2 (2x 2 − 1))57. y =tgx.(DS. 2 sin xcos3x)58. y =√1+x 2 .(DS.1(1 + x 2 )3 /2 )59. y = arcsinx 2 .(DS.x(4 − x 2 )3 /2 )60. y = arctg1x.(DS.2x(1 + x 2 ) 2 )70 ... la.idˆe`u=0v`ıx 2 (k)=0 ∀k> ;2. ´Ap du.ng cˆong th´u.c(cos 2x)(n) =2 ncos2x +nπ 2 ta thu du.o..c(x 2 cos 2x)(n) =2 nx 2 −n(n − 1)4cos2x +nπ 2  +2 nnx sin2x +nπ 2 . ... du.o..c1a 2 −1b 2 yx 2 −yb 2 yxx=0v`a t`u.(8 .2) ta thu du.o..c yx:yxx=1yb 2 a 2 −yx 2 =1yb 2 a 2 −b4a4x 2 y 2 = −b4a 2 y3x 2 a 2 −y 2 b 2 = −b4a 2 y3,y>0. V´ı...

Bài tập toán cao cấp part 6 doc

... x 2 ]dx= 2 cos x 2 dx +2x(−sin x 2 )2xdxdx= (2 cos x 2 − 4x 2 sin x 2 )dx 2 .Phu.o.ng ph´ap II.T´ınh da.o h`am cˆa´p hai fxxta c´ofx=2x cos x 2 ,fxx= 2 cos x 2 − ... x 2 dx)=(2x cos x 2 )d 2 x +[d(2x cos x 2 )]dx=2x cos x 2 d 2 x + (2 cos x 2 − 4x 2 sin x 2 )dx 2 . V´ı d u.3.´Ap du.ng vi phˆan dˆe’t´ınh gˆa`nd´ung c´ac gi´a tri.:1)5 2 −0, 15 2+ 0, ... tgx1cos x= 2 limx→π 2 1cos 2 x ·tgx+ sin xcos 2 x= 2 limx→π 2 1cos xtg 2 x= 2 limx→π 2 −sin xcos 2 x2tgx ·1cos 2 x= limx→π 2 cos x =0.Do d´olimx→π 2 tgx 2 cos x=...

Bài tập toán cao cấp part 7 pot

... o(t 2 )=−x 2 2+x4 24 + o(x4) −1 2 −x 2 2+x44+ o(x4) 2 + o−x 2 2+x4 24 + o(x4) 2 = −x 2 2+x4 24 −x48+ o(x4)=−x 2 2−x4 12 + o(x4). V´ı du.5. ... ln(x 2 +3x + 2) .(DS. ln2 +nk=1(−1)k−1k(1 + 2 −k)xk+ o(xn))6. f(x) = ln (2 + x −x 2 ). (DS. ln2 +nk=1(−1)k−1− 2 −kkxk+ o(xn))7. f(x)=1 − 2x 2 2+x − x 2 .(DS.1 2 +nk=1(−1)k+1− ... nhiˆe`ubiˆe´n 125 9 .2. 1 Vi phˆan cˆa´p1 126 9 .2. 2´Ap du.ng vi phˆan dˆe’t´ınh gˆa`nd´ung . . . . . 126 9 .2. 3 C´ac t´ınh chˆa´tcu’aviphˆan 127 9 .2. 4 Vi phˆan cˆa´pcao 127 9 .2. 5 Cˆong...

Bài tập toán cao cấp part 8 doc

... nhiˆe`ubiˆe´n 2) Ta c´o∂w∂x=yx 2 + y 2 ,∂w∂y= −xx 2 + y 2 ·T`u.d´o∂ 2 w∂x 2 =∂∂xyx 2 + y 2 = −2xy(x 2 + y 2 ) 2 ,∂ 2 w∂y 2 =∂∂y−xx 2 + y 2 =2xyx 2 + y 2 ,∂ 2 w∂x∂y=∂∂yyx 2 + ... at),∂ 2 u∂t 2 = a 2 ∂ 2 u∂x 2 41. u = xf(x + y)+yg(x + y),∂ 2 u∂x 2 2 ∂ 2 u∂x∂y+∂ 2 u∂y 2 =0. 42. u = fyx+ xgyx, x 2 ∂ 2 u∂x 2 +2xy∂ 2 u∂x∂y+ y 2 ∂ 2 u∂y 2 =0.43. ... y 2 ,∂ 2 w∂x∂y=∂∂yyx 2 + y 2 =x 2 − y 2 (x 2 + y 2 ) 2 ,∂ 2 w∂y∂x=∂∂x−xx 2 + y 2 =x 2 −y 2 (x 2 + y 2 ) 2 ·Nhˆa.nx´et. Trong ca’1) lˆa˜n2)tadˆe`uc´o∂ 2 w∂x∂y=∂ 2 w∂y∂x. V´ı...

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