.-. is, -s- |s. iss. .- |s :s ?.s+ .s.. ...>- s ss. ..- ..s.> u? M.s Q.s. Bi 1: Tnh cc gii hn sau: 1. -+- -22xx 1lim1 3x 5x2.22x3x(2x 1)lim(5x 1)(x 2x)--- + 3. 33 23 2 2lim2 2 1xx xx x- +- + -4. 3 243 2 1lim4 3 2xx xx x- -+ - 5. 2 24x(x 1) (7x 2)lim(2x 1)- ++6. 2 32 2x(2x 3) (4x 7)lim(3x 4) (5x 1)- +- - 7. 23 2lim3 1xx x xx-- +-8.3 3 2 2 3 2 232( 2 ) 2lim3 2xx x x x x xx x-+ + + +- 9. x(x x x 1)( x 1)lim(x 2)(x 1) ++ - ++ -10. 22 xx x 2 3x 1lim4x 1 1 x+ + + ++ + - Bi 2: Tnh cc gii hn sau: 1.) 2 3 ( lim2x x xx- + -+ 2. 2xlim (2x 1 4x 4x 3)- - - -3. 2 2xlim ( x 4x 3 x 3x 2)- + - - + 4. 2xlim (3x 2 9x 12x 3)+ - + -5.) 2 2 3 ( lim2- + + -+ x x xx6. 3 2 3xlim ( x 1 x 1)++ - -7. 3 3 2lim( 2 1 3 )xx x x x+ - - - 8. 22 xx x 2 3xlim4x 1 x 1+ + ++ - + 9. 23 3 xx 2x 3limx x 1+ +- +10. 1 x x1 x x 1 x xlim22 2x+ ++ - + + + Bi 3: Tnh cc gii hn sau: 1. 1 x x 16 x 14 1x 7lim2 x+ + + + 2. xlim x x x x+ + + - 3. ( )2 2xlim x x 2x 2 x x x++ - + + 4. ( ) ( )nn nxxx x x x 1 1lim2 2- + - - -+ 5. - - - + ++ x x x x x xxlim 6. ( ) 1 1 .1lim- - ++ x x xx 7.( ) 1 3 . lim - - ++ x x xx8.( )3 2 3 3 2 31 1 lim + - - + + x x x xx 9.( ) x x x x xx+ + - ++ 2 22 2 lim 10.( ) x x xx+ - - ++ 1 2 2 limBi 4: Tnh cc gii hn sau: 1. - + ++ x x x xx3 3 3 3 lim 2. 3 3 2 2xlim ( 8x 2x 4x 2x 4x 1)+ + + - +3. 3 4 3 2 6 52xx 2x 3x x 6xlimx 2x 4- + - ++ + 4. 3 2 3 22xx 2x 3 x 6xlimx x 2x 4- + - ++ + + .-. is, -s- |s. iss. .- |s :s ?.s+ .s.. ...>- s ss. ..- ..s.> u? M.s Q.s. 5. 3 2 2 3 24 3 2xx 2x( 4x 3x 3 x 3xlim4x 2x 4x+ - + - ++ + 6. 3 4 3 6 52xx 2x x 6xlimx x 2x 4- - ++ + + 7. 3 4 3 2 6 53 3 2x4x 3x 3x 8x 2xlimx x 2x- + - +- + 8. 3 4 3 2 6 52xx 2x 3x x 6xlim2x 1 x 2x 4- + - ++ + + + 9. 3 4 3 2 6 52x16x 2x 3x 8x 2xlim(x 2)(x x 2x 4)- + - ++ - + + 10. 3 4 3 6 52x4x 2x 8x 6xlim3x 1 9x 2x 4- - +- + + + Bi 5: Tnh cc gii hn sau: 1. 222lim3 1xx xx--+2. 2 3x 0x xlim2x++ 3. 2 3x 02xlim4x x+4. 23 3lim22- + --xx xx 5. 23 3lim222- ++ --- x xx xx6. 32x 1x 3x 2limx 5x 4-- +- + 7. x 01 xlim xx - 8. 2x 1x x 2limx 1++ -- 9. 23x 2x 4x 1limx 3x 2- +- +10. 23 2x 13x 7x 1limx x 4x 4+ -- - + Bi 6: Tm gii hn bn phi, gii hn bn tri ca f(x) tixo v xt xem hm s c gii hn ti xo khng : 1. - +>-= =- 22ox 3x 2 (x 1)x 1f(x) vix 1x (x 1)2 2. - + -= =o vixx+ .-. is, -s- |s. iss. .- |s :s ?.s+ .s.. ...>- s ss. ..- ..s.> u? M.s Q.s. 4. 20x 3x 4 khix1f (x) (x 1)2x3khi x 1 - + < = =- 5. 320x x 6 khi x 2x x 2f (x) (x 2)11khi x 23- -- -= == 6. 0sin xkhi x 1f (x) (x 1) x 1khi x 1p = = --p = 7. 3201 cosxkhi x 0sin xf (x) (x 0)1khi x 06 -= == 8. 220 0x 3x 10 khi x 2x 42x 3f ( x) khi 2 x 5 ( x 2; x 5)x 23x 4khi x5+ - 9. 2220 032x 3x 5 x 2(x 3)x 9f (x) 2x x 1 ( 3 x 2) (x 3; x 2)x 8(x 2)x 4+ + - - < --= - + - = - =->- 10. 3 3220 042x 3x 4 3x 1(x 2)x 4f (x) 2x x 1 ( 1 x 2) (x 2; x 1)x 4x 4 x 4(x 1)x 1+ + - + >-= + - - = = -+ + - -< -- Bi 7: Tm cc gi tr ca tham s cc hm s sau lin tc trn R: 1. 23x 2x 1 khix1f (x)2x akhi x 1 + - < =+ .-. is, -s- |s. iss. .- |s :s ?.s+ .s.. ...>- s ss. ..- ..s.> u? M.s Q.s. 2. 32x 2x 3 khix1x 1f (x) akhi x 1ax 2b 1 khi x 1 + --= =+ - = - 3. 1 cos4xkhi x 0x.sin 2xf (x) (x 0)x akhi x 0x 1 - 8. 2x khix1f (x) ax b khi 1 x 34 x khi x 3 9. 3 22x 6 2x 9A x 3f (x) (x 3)x 4x 3x3x 2 x 3+ + -+ - s ss. ..- ..s.> u? M.s Q.s. 10. 3 3220 042x 3x 4 3x 1(x 2)x 4f (x) ax (a b)x a b ( 1 x 2) (x 2; x 1)x 4x 4 x 4(x 1)x 1+ + - + >-= + + - + - = = -+ + - -< -- Bi 8: Chng minh s tn ti nghim ca cc phng trnh sau, km theo cc iu kin ch ra: 1. x3 2x 7 = 02. x5 + x3 1 = 0 3. x5 + 7x4 3x2 + x + 2 = 04. cosx x + 1 = 0 5. x3 3x2 + 3 = 0 c 3 nghim trong khong ( 1;3) 6. 2x3 6x + 1 = 0 c 3 nghim trong khong ( 2;2) 7. x5 5x4 + 4x 1 = 0 c 3 nghim trong khong (0;5) 8. Cho 3 s a,b,c khc nhau .Chng minh rng phng trnh:(x a)(x b) + (x b)(x c) + (x c)(x a) = 0 c 2 nghim phn bit. 9. Cho f(x) = ax2 + bx + ctho mn : 2a + 6b + 19c = 0. Chng minh rng phng trnh ax2 + bx + c = 0 c nghim trong [0;1] 10. Cho f(x) = ax2 + bx + ctho mn : 2a + 3b + 6c = 0. Chng minh rng phng trnh ax2 + bx + c = 0 c nghim trong (0;1) Bi 9: Chng minh s tn ti nghim ca cc phng trnh sau, km theo cc iu kin ch ra: 1. Cho hm s f(x ) lin tc trn on [a;b] thof(x) [a;b] " x [a;b] Chng minh rng phng trnh:f(x) = x c nghim x [a;b]. 2. cosx + m.cos2x = 0 lun c nghim. 3. m(x 1)3(x + 2) + 2x + 3 = 0 lun c nghim. 4. a(x b)(x c) + b(x c)(x a) + c(x a)(x b) = 0 lun c nghim. 5. (m2 + m + 1)x4 + 2x 2 = 0 lun c nghim. 6. Cho phng trnh x4 x 3 = 0. Chng minh rng: phng trnh c nghim xo (1;2) v xo >7,127. 8. 9. 10. Bi 1: Tnh cc gii hn sau: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. .-. is, -s- |s. iss. .- |s :s ?.s+ .s.. ...>- s ss. ..- ..s.> u? M.s Q.s.