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... 27,9g muối khan . dd B. Cô cạn dd B thu được 27,9g muối khan .  Phần 2 : Cho vào 800ml dd HCl xM và làm tương Phần 2 : Cho vào 800ml dd HCl xM và làm tương tự thu được 32,35g muối khan . tự thu ... gam hh X hòa tan trong nước dư thì thu TN1: Đem m gam hh X hòa tan trong nước dư thì thu được 0,2 mol H được 0,2 mol H 2 2 thoát ra . thoát ra .  TN2: Đem m gam hh X hòa tan trong dd KOH ... gam hh X hòa tan trong dd KOH dư thí thu được 0,35 mol H thu được 0,35 mol H 2 2 thoát ra . thoát ra .  TN3: Đem m gam hh X hòa tan trong dd HCl dư thì TN3: Đem m gam hh X hòa tan trong dd...

... r˘a ` ng 1) cos π 9 + cos 3π 9 + cos 5π 9 + cos 7π 9 = 1 2 . 2) cos ϕ + cos(ϕ + α)+cos(ϕ +2α)+···+ cos(ϕ + nα) = sin (n +1)α 2 cos  ϕ + nα 2  sin α 2 · Gia ’ i. 1) D ˘a . t S = cos π 9 + cos 3π 9 + ... Khi d ´o cos α = 1 + cos ϕ −2 cos ϕ 2 = − cos ϕ 2 = cos  ϕ 2 − π  , sin α = sin ϕ −2 cos ϕ 2 = − sin ϕ 2 = sin  ϕ 2 − π  . T`u . d ´o suy r˘a ` ng 1 + cos ϕ + i sin ϕ = −2 cos ϕ 2  cos  ϕ 2 − ... +1)ϕ] a 2 − 2a cos ϕ +1 + −a cos ϕ + ai sin ϕ +1 a 2 − 2a cos ϕ +1 = a n+2 cos nϕ − a n+1 cos(n +1)ϕ− a cos ϕ +1 a 2 − 2a cos ϕ +1 + + i a n+2 sin nϕ− a n+1 sin(n +1)ϕ + a sin ϕ a 2 − 2a cos ϕ +1 · B˘a ` ng...

... lim x→0 m √ cos αx− m √ cos βx x 2 (DS. β 2 − α 2 2m ) 54. lim x→0 cos x− 3 √ cos x sin 2 x (D S. − 1 3 ) 55. lim x→0 1 − cos x √ cos 2x tgx 2 (DS. 3 2 ) 56. lim x→0 √ 1+x sin x − cos x sin 2 x 2 (D S. ... 39 48. lim x→0 √ cos x − 1 x 2 (DS. − 1 4 ) 49. lim x→ π 2 cos x 2 − sin x 2 cos x (D S. 1 √ 2 ) 50. lim x→ π 3 sin  x − π 3  1 − 2 cos x (D S. 1 √ 3 ) 51. lim x→ π 4 √ 2 cos x− 1 1 − tg 2 x (D S. 1 4 ) 52. ... x 0 =1l`adiˆe ’ m gi an doa . nkiˆe ’ uI. V´ı d u . 6. X´ac d i . nh v`a ph an loa . idiˆe ’ m gi an doa . ncu ’ a h`am f(x)=              x cos 1 x khi x<0 0 khi x =0 cos 1 x khi x>0. 2MU . CLU . C 8.2.2...

... T´ıch ph an bˆa ´ td i . nh 2)  1 + cos 2 x 1 + cos 2x dx =  1 + cos 2 x 2 cos 2 x dx = 1 2   dx cos 2 x +  dx  = 1 2 (tgx + x)+C. 3)  √ 1 − sin 2xdx =   sin 2 x− 2 sin x cos x + cos 2 xdx =   (sin ... cˆong th´u . c t´ıch ph an t`u . ng phˆa ` n ta c´o I = −xcotgx +  cotgxdx = −xcotgx +  cos x sin x dx = −xcotgx +  d(sin x) sin x = −xcotgx +ln| sin x| + C. 2) T´ıch ph an I n du . o . . cbiˆe ’ udiˆe ˜ ndu . ´o . ida . ng I n = 1 a 2  x 2 + ... I 2 =  sin x cos 3 x 1 + cos 2 x dx. Gia ’ i 1) C´ach I.Tac´o  dx sin x =  sin x sin 2 x dx =  d(cos x) cos 2 x − 1 = 1 2 ln 1 − cos x 1 + cos x + C. C´ach II.  dx sin x =  d  x 2  sin x 2 cos x 2 =  d  x 2  tg x 2 ·...

... m 2 )) 44. lim x→∞ x 2  cos 1 x − cos 3 x  (D S. 4) 45. lim x→0 sin(a + x) + sin(a − x) − 2 sin a x 2 (DS. − sin a) 46. lim x→0 cos(a + x) + cos(a − x) − 2 cos a 1 − cos x (D S. −2 cos a) 47. lim x→∞  sin √ x 2 +1− ... − 4. 2) D ˘a . t y = π 4 − x. Khi d ´o lim x→ π 4 cotg2x · cotg  π 4 − x  = lim y→0 cotg  π 2 − 2y  cotgy = lim y→0 sin 2y sin y · cos y cos 2y =2. 7.2. Gi´o . iha . n h`am mˆo . tbiˆe ´ n ... x 0 =1l`adiˆe ’ m gi an doa . nkiˆe ’ uI. V´ı d u . 6. X´ac d i . nh v`a ph an loa . idiˆe ’ m gi an doa . ncu ’ a h`am f(x)=              x cos 1 x khi x<0 0 khi x =0 cos 1 x khi x>0. 24...

... m 2 )) 44. lim x→∞ x 2  cos 1 x − cos 3 x  (D S. 4) 45. lim x→0 sin(a + x) + sin(a − x) − 2 sin a x 2 (DS. − sin a) 46. lim x→0 cos(a + x) + cos(a − x) − 2 cos a 1 − cos x (D S. −2 cos a) 47. lim x→∞  sin √ x 2 +1− ... − 4. 2) D ˘a . t y = π 4 − x. Khi d ´o lim x→ π 4 cotg2x · cotg  π 4 − x  = lim y→0 cotg  π 2 − 2y  cotgy = lim y→0 sin 2y sin y · cos y cos 2y =2. Chu . o . ng 7 Gi´o . iha . nv`aliˆen tu . ccu ’ a h`am ... . 126 9.2.3 C´ac t´ınh chˆa ´ tcu ’ a vi ph an . . . . . . . . . . . . 127 9.2.4 Vi ph an cˆa ´ pcao 127 9.2.5 Cˆong th´u . cTaylor 129 9.2.6 Vi ph an cu ’ a h`am ˆa ’ n 130 9.3 Cu . . c tri . cu ’ a...

... = 1 (vˆo l´y) . 1 Ch ’ u ’ ong 2. Khˆong gian ¯di . nh chu ’ an 10. Cho A, B l`a hai to an t ’ ’ u t´ıch ph an trong C [a,b] v ´ ’ oi ha . ch l ` an l ’ u ’ o . t l`a K(t, s), H(t, s) Ax(t) ... s)ds. Ch ’ u ’ ong 4. C´ac nguyˆen l´ı c ’ o b ’ an c ’ ua gi ’ ai t´ıch h`am 5. Cho X, Y l`a c´ac khˆong gian ¯di . nh chu ’ an, M ⊂ X, v`a f : M → Y sao cho f(M) compact. Ch ´ ’ ung minh n ´ ˆeu G A = ... t ’ u . l ´ ˆay t´ıch ph an ta ¯d ’ u ’ o . c BAx(t) = b  a  b  a H(t, u)K(u, s)x(s)du  ds = b  a (H(t, u)K(u, s)du) x(s)ds. Vˆa . y B ◦ A l`a to an t ’ ’ u t´ıch ph an v`a ha . ch b  a H(t,...

... m 2 )) 44. lim x→∞ x 2  cos 1 x − cos 3 x  (D S. 4) 45. lim x→0 sin(a + x) + sin(a − x) − 2 sin a x 2 (DS. − sin a) 46. lim x→0 cos(a + x) + cos(a − x) − 2 cos a 1 − cos x (D S. −2 cos a) 47. lim x→∞  sin √ x 2 +1− ... lim x→0 m √ cos αx − m √ cos βx x 2 (DS. β 2 − α 2 2m ) 54. lim x→0 cos x − 3 √ cos x sin 2 x (D S. − 1 3 ) 55. lim x→0 1 − cos x √ cos 2x tgx 2 (DS. 3 2 ) 56. lim x→0 √ 1+x sin x − cos x sin 2 x 2 (D S. ... − 4. 2) D ˘a . t y = π 4 − x. Khi d ´o lim x→ π 4 cotg2x · cotg  π 4 − x  = lim y→0 cotg  π 2 − 2y  cotgy = lim y→0 sin 2y sin y · cos y cos 2y =2. 26 Chu . o . ng 7. Gi´o . iha . n v`a liˆen...

... r˘a ` ng 1) cos π 9 + cos 3π 9 + cos 5π 9 + cos 7π 9 = 1 2 . 2) cos ϕ + cos(ϕ + α)+cos(ϕ +2α)+···+ cos(ϕ + nα) = sin (n +1)α 2 cos  ϕ + nα 2  sin α 2 · Gia ’ i. 1) D ˘a . t S = cos π 9 + cos 3π 9 + ... cos 2π 5 + cos 4π 5 = − 1 2 4) cos 2π 7 + cos 4π 7 + cos 6π 7 = − 1 2 5) cos 2π 9 + cos 4π 9 + cos 6π 9 + cos 8π 9 = − 1 2 L`o . i n´oi d ˆa ` u Gi´ao tr`ınh B`ai tˆa . p to an cao cˆa ´ p n`ay du . o . . c ... +1)ϕ] a 2 − 2a cos ϕ +1 + −a cos ϕ + ai sin ϕ +1 a 2 − 2a cos ϕ +1 = a n+2 cos nϕ − a n+1 cos(n +1)ϕ− a cos ϕ +1 a 2 − 2a cos ϕ +1 + + i a n+2 sin nϕ − a n+1 sin(n +1)ϕ + a sin ϕ a 2 − 2a cos ϕ +1 · B˘a ` ng...

... 1: ) 1 .( 1 )tan 1 tan.( 1 )tan 1 tan( tan 1 tan )tan 1 tan( )tan 1 tan).(tan 1 tan( tan 1 tan 2 2 2 2 2 2 22 2 2 22 2 2 2 lim lim lim limlim Cosx Sinx CosxxCos xSin Cosx x Cosx xCosx x Cosx x x Cosx x x Cosx x x Cosx xx Cosx x x Cosx x x x x xx ++ = ++ = ++ −+ = ++ ++−+ =         −+ → → → →→ π π π ππ 2 1 101 1 )( 1 ).( 1 ) 1 .( 1 2 2 2 2 2 2 2 2 lim limlim = ++ = ++ = + + = ++ → →→ SinxCosxxSin Cosx Sinx xCos CosxxSin Cosx Cosx Sinx CosxxCos xSin Cosx x xx π ππ Nguyễn ... 2.( 2 1 2 1 ).( 2 2 0 3 4 3 22 2 2 0 3 4 3 222 23 0 2 3 2 0 3 2 3 2 0 2 3 0 lim lim lim limlimlim −=−= ++ −− = ++ − = − = + − = − → → → →→→ x x xCosxCosCosxxCos xCos xSin Cosx xCosxCosCosxxCosxSin xCosxCos xSin xCosCosx CosxCosxxSin xCosCosx xSin CosxCosx x x x xxx Bài 8: 4)11.(2 )11.(2 )11.(2 )11).(21()11).(12( 11 12 2 2 2 0 2 2 2 0 2 22 0 2 2 0 2 2 0 2 0 lim limlim limlimlim =+−= +−= +− = +−− = − +−− = −− − → →→ →→→ x x x x x xSin x xxSin x xxCos x xxCos x xCos x xx xxx Bài ... ) 8 1 ) 2 1 4 1 .( 2 1 ) 2 ( 2 ) 2 ( .1. 2 1 2 2 2 22 1 2 2 ).2( . 21 1 . 2 tan )2( . 21 1 21. 2 tan 2 21. 2 tan 21 21. 2 tan )21).(21( 2 tan 21 2 2 0 2 2 0 2 2 0 2 0 2 0 2 22 00 2 2 00 2 2 0 2 0 2 0 2 0 limlim limlimlim limlim limlim lim lim limlim −=−=             −=             −= + ++ = + ++ = ++ + = ++ −+ = ++ ++−+ = −+ →→ →→→ →→ →→ → → →→ x x x x x Sin xSin x Sin xSinxx Cos x Sin x CosxSinxSinx xCosxSinx x xSinxSinx xCosxSinx xCosxSinx x xSinxSinx xCosxSinx x xCosxSinx xCosxSinx x xCosxSinxxCosxSinx x xCosxSinx XX XXX XX XX X X XX Nguyễn Phan Thanh Lâm...

... r˘a ` ng 1) cos π 9 + cos 3π 9 + cos 5π 9 + cos 7π 9 = 1 2 . 2) cos ϕ + cos(ϕ + α)+cos(ϕ +2α)+···+ cos(ϕ + nα) = sin (n +1)α 2 cos  ϕ + nα 2  sin α 2 · Gia ’ i. 1) D ˘a . t S = cos π 9 + cos 3π 9 + ... −π<ϕ<π⇒− π 2 < ϕ 2 < π 2 ⇒ cos ϕ 2 > 0. Gia ’ su . ’ α = argz. Khi d ´o cos α = 1 + cos ϕ 2 cos ϕ 2 = cos ϕ 2 , sin α = sin ϕ 2 cos ϕ 2 = sin ϕ 2 ·            ⇒ z = 2 cos ϕ 2  cos ϕ 2 + i sin ϕ 2  . 28 ... +1)ϕ] a 2 − 2a cos ϕ +1 + −a cos ϕ + ai sin ϕ +1 a 2 − 2a cos ϕ +1 = a n+2 cos nϕ − a n+1 cos(n +1)ϕ− a cos ϕ +1 a 2 − 2a cos ϕ +1 + + i a n+2 sin nϕ − a n+1 sin(n +1)ϕ + a sin ϕ a 2 − 2a cos ϕ +1 · B˘a ` ng...

... r˘a ` ng 1) cos π 9 + cos 3π 9 + cos 5π 9 + cos 7π 9 = 1 2 . 2) cos ϕ + cos(ϕ + α)+cos(ϕ +2α)+···+ cos(ϕ + nα) = sin (n +1)α 2 cos  ϕ + nα 2  sin α 2 · Gia ’ i. 1) D ˘a . t S = cos π 9 + cos 3π 9 + ... =  2(1 + cos ϕ)=2    cos ϕ 2    = −2 cos ϕ 2 v`ı π 2 < ϕ 2 <π. Gia ’ su . ’ α = argz. Khi d ´o cos α = 1 + cos ϕ −2 cos ϕ 2 = − cos ϕ 2 = cos  ϕ 2 − π  , sin α = sin ϕ −2 cos ϕ 2 = ... +1)ϕ] a 2 − 2a cos ϕ +1 + −a cos ϕ + ai sin ϕ +1 a 2 − 2a cos ϕ +1 = a n+2 cos nϕ − a n+1 cos(n +1)ϕ− a cos ϕ +1 a 2 − 2a cos ϕ +1 + + i a n+2 sin nϕ− a n+1 sin(n +1)ϕ + a sin ϕ a 2 − 2a cos ϕ +1 · B˘a ` ng...

... m 2 )) 44. lim x→∞ x 2  cos 1 x − cos 3 x  (D S. 4) 45. lim x→0 sin(a + x) + sin(a − x)− 2 sin a x 2 (DS. − sin a) 46. lim x→0 cos(a + x) + cos(a − x) − 2 cos a 1 − cos x (D S. −2 cos a) 47. lim x→∞  sin √ x 2 +1− ... − 4. 2) D ˘a . t y = π 4 − x. Khi d ´o lim x→ π 4 cotg2x · cotg  π 4 − x  = lim y→0 cotg  π 2 − 2y  cotgy = lim y→0 sin 2y sin y · cos y cos 2y =2. 7.1. Gi´o . iha . ncu ’ a d˜ay sˆo ´ 5 Hˆe . th´u . c ... x 0 =1l`adiˆe ’ m gi an doa . nkiˆe ’ uI. V´ı d u . 6. X´ac d i . nh v`a ph an loa . idiˆe ’ m gi an doa . ncu ’ a h`am f(x)=              x cos 1 x khi x<0 0 khi x =0 cos 1 x khi x>0. 7.2....

... ) sin , 1 cos ,0 2x a t t y a t t π = − = − ≤ ≤ ĐS: 2 2 a π − 13 BỘ MÔN KHOA HỌC CƠ BẢN – MÔN TOÁN CAO CẤP II ĐS: 5 3 ln 4 + 10. ( ) 2 2 2 + + ∫ C x y z ds , C là cung đường cong cos , sin ... (1, 0), (1, 2) ĐS: 2 17. cos sin C ydx xdy− ∫Ñ , C là đoạn thẳng từ điểm (2, -2) đến điểm (-2, 2) ĐS: 2sin 2− 18. ( ) ( ) 2 2 2 2 C x y dx x y dy+ + − ∫Ñ , C là đường cong 1 |1 |,0 2y x x= − ... đường xicloid ( ) ( ) sin , 1 cos , 0x a t t y a t a= − = − > có định hướng tăng của tham số ĐS: ( ) 3 5 2a π π − 14 BỘ MÔN KHOA HỌC CƠ BẢN – MÔN TOÁN CAO CẤP II 64.Phần mặt paraboloid...

... Ngu ̃   D                                                    4+ 4+ 4+ 4+4+4+ −=−= ++ −− = ++ − = − = + − = − → → → →→→ x x xCosxCosCosxxCos xCos xSin Cosx xCosxCosCosxxCosxSin xCosxCos xSin xCosCosx CosxCosxxSin xCosCosx xSin CosxCosx x x x xxx EF                          4+ 4+4+ 4+4+4+ =+−= +−= +− = +−− = − +−− = −− − → →→ →→→ x x x x x xSin x xxSin x xxCos x xxCos x xCos x xx xxx   G                       4+4+ 4+4+4+       4+              −=       + +−= + +− =                 + −=       + −=         + + +∞→+∞→ +∞→ + +∞→ + +∞→ + +− +∞→ + + − + − xx x xxx x xx x x x x x x x x x x x e 3  4        4+ − + +∞→ =         + + e x x x x Nguyê ̃ n ...      4+ −− − → x xCos x        4+ + +∞→         + + x x x x  Sinx x Sinx x    ) 4+       + + →        4+ − +∞→         −+ −+ x x xx xx        )  )  )  ) )  ) )  ) )  ))  ) )  )              4+ 4+ 4+ 4+4+ Cosx Sinx CosxxCos xSin Cosx x Cosx xCosx x Cosx x x Cosx x x Cosx x x Cosx xx Cosx x x Cosx x x x x xx ++ = ++ = ++ −+ = ++ ++−+ =         −+ → → → →→ π π π ππ                     4+ 4+4+ = ++ = ++ = + + = ++ → →→ SinxCosxxSin Cosx Sinx xCos CosxxSin Cosx Cosx Sinx CosxxCos xSin Cosx x xx π ππ Nguyê ̃ n Phan Thanh Lâm MSV: 071250510319 Trang 14/20 Ba ̀ i tâ ̣ p toa ́ n cao cấp I GVHD: Phan Thi ̣ ... )                                  )       )    )    )   )                              4+4+ 4+4+4+ 4+4+ 4+4+ 4+ 4+ 4+4+ −=−=             −=             −= + ++ = + ++ = ++ + = ++ −+ = ++ ++−+ = −+ →→ →→→ →→ →→ → → →→ x x x x x Sin xSin x Sin xSinxx Cos x Sin x CosxSinxSinx xCosxSinx x xSinxSinx xCosxSinx xCosxSinx x xSinxSinx xCosxSinx x xCosxSinx xCosxSinx x xCosxSinxxCosxSinx x xCosxSinx XX XXX XX XX X X XX Nguyê ̃ n Phan Thanh Lâm...