Bài tập toán cao cấp part 2 pdf

... hˆo . itu . 1) a n = n 2 − 1 n 2 2) a n =2+ 1 2! + 1 3! + ···+ 1 n! Chı ’ dˆa ˜ n. T´ınh bi . ch˘a . ndu . o . . csuyt`u . n!  2 n−1 v`a do d´o a n  2+ 1 2 + 1 2 2 + ···+ 1 2 n−1 =3− 1 2 n−1 < 3. 4. ... c´o: a n+1 = √ 2a n ⇒ a 2 n+1 =2a n . Do d ´o: lim a 2 n+1 = 2 lima n hay a 2 − 2a = 0 v`a thu du . o . . c a 1 =0,a 2 =2. V`ı d˜ay d o . ndiˆe . u t˘ang ∀n...

Ngày tải lên: 13/07/2014, 23:20

... dw.Tac´o (6xy + w − 2) dx +(3x 2 +2yw 2 +1)dy +(3w 2 + x +2y 2 w)dw =0 v`a do d ´o dw = 2 − 6xy − w 3w 2 + x +2y 2 w dx − 3x 2 +2yw 2 +1 3w 2 + x +2y 2 w dy.  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 +...

Ngày tải lên: 13/07/2014, 23:21

... + − ∫ ∫ =0 ( ) ( ) 2 2 2 2 1 1 1 1 4 1 1 | 1 2 1 2 2 2 2 y y J x dy y dy y       = = − = − = − − − =  ÷  ÷  ÷       ∫ ∫ 4 4 4 2 2 2 2 2 2 16 4 | 2 2 8 4 1 2 4 4 4 y y y K x ... 1 2 1 2 1 t dt dt t t t t + − ⇔ = + + ∫ ∫ 2 2 1 1 1 1 1 ln | | ln | 1| ln | | ln | 1| 2 1 2 2 2 2 dt dt t t u u t t   ⇔ − = − + = − +  ÷ +   ∫ ∫ (2) Thay (1) và...

Ngày tải lên: 03/07/2014, 18:21

... b)(a 2 − ab + b 2 ) suy ra a n =  3 √ n 2 − n 3 + n  3 √ n 2 − n 3  2 − n 3 √ n 2 − n 3 + n 2   3 √ n 2 − n 3  2 − n 3 √ n 2 − n 3 + n 2 = n 2  3 √ n 2 − n 3  2 − n 3 √ n 2 − n 3 + 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 a n du . ´o . ida . ng a n =0, 22 2= 2 10...

Ngày tải lên: 13/07/2014, 23:20

... (15 -26 ) 15. lim x→0 √ 1+x + x 2 − 1 x (DS. 1 2 ) 16. lim x 2 √ 3+x + x 2 − √ 9 − 2x + x 2 x 2 − 3x +2 (DS. 1 2 ) 17. lim x→0 5x 3 √ 1+x − 3 √ 1 − x (D S. 15 2 ) 18. lim x→0 3 √ 1+3x − 3 √ 1 − 2x x ... gi´o . iha . n sau dˆay (3-10). 3. lim x→7 2x 2 − 11x − 21 x 2 − 9x +14 (DS. 17 5 ) 4. lim x→1 x 4 −x 3 + x 2 − 3x +2 x 3 −x 2 − x +1 (DS. 2) 5. lim x→1 x 4 +2x 2...

Ngày tải lên: 13/07/2014, 23:20

... 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 −...

Ngày tải lên: 13/07/2014, 23:20

... e −x 2 .(DS. 2e −x 2 (2x 2 − 1)) 57. y =tgx.(DS. 2 sin x cos 3 x ) 58. y = √ 1+x 2 .(DS. 1 (1 + x 2 ) 3 /2 ) 59. y = arcsin x 2 .(DS. x (4 − x 2 ) 3 /2 ) 60. y = arctg 1 x .(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 n cos  2x + nπ 2  ta thu du . o . . c (x 2 cos 2x) (n) =2 n  x 2 −...

Ngày tải lên: 13/07/2014, 23:20

... 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  xx ta c´o f  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 d ˆe ’ t´ınh gˆa...

Ngày tải lên: 13/07/2014, 23:20

... o(t 2 ) =  − x 2 2 + x 4 24 + o(x 4 ) − 1 2  − x 2 2 + x 4 4 + o(x 4 )  2  + o   − x 2 2 + x 4 24 + o(x 4 )  2  = − x 2 2 + x 4 24 − x 4 8 + o(x 4 )=− x 2 2 − x 4 12 + o(x 4 ).  V´ı du . 5. ... ln(x 2 +3x + 2) . (DS. ln2 + n  k=1 (−1) k−1 k (1 + 2 −k )x k + o(x n )) 6. f(x) = ln (2 + x −x 2 ). (DS. ln2 + n  k=1 (−1) k−1 − 2 −k k x k + o(x n )) 7....

Ngày tải lên: 13/07/2014, 23:20

... nhiˆe ` ubiˆe ´ n 2) Ta c´o ∂w ∂x = y x 2 + y 2 , ∂w ∂y = − x x 2 + y 2 · T`u . d ´o ∂ 2 w ∂x 2 = ∂ ∂x  y x 2 + y 2  = − 2xy (x 2 + y 2 ) 2 , ∂ 2 w ∂y 2 = ∂ ∂y  −x x 2 + y 2  = 2xy x 2 + y 2 , ∂ 2 w ∂x∂y = ∂ ∂y  y x 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...

Ngày tải lên: 13/07/2014, 23:20