PHIU S 1N TP HM SBi ton tip tuyn c bn: 7. Cho hm s 2 32 3+ x x y vit phng trnh tip tuyn bit tip tuyn qua A(-1;-2).8. Cho hm s ( )34 3 x x x f y vit phng trnh tip tuyn ca th hm s bit tip tuyn i qua: M(1;3). 9. Cho hm s ( )22 3++ xxx f y. Vit phng trnh tip tuyn bit tip qua A(1;3).10. Cho hm s ( )xx xx f y12+ . Vit phng trnh tip tuyn qua A(2;-1). 11. Cho hm s ( )2 42121x x x f y . Vit phng trnh tip tuyn bit tip tuyn qua gc O(0;0).12. Cho hm s x x y 33 a) Chng minh rng khi m thay i, ng thng ( ) 2 1+ + x m y lun ct th (1) ti mt im A c nh. b) Tm m ng thng ct (1) ti 3 im A, B, C khc nhau sao cho tip tuyn ti B v C vung gc vi nhau. 13. Cho hm s xx xy2 32+ tm trn ng thng x =1. Nhng im M sao cho t M k c hai tip tuyn ti (C) m hai tip tuyn vung gc. * n tp cng thc tnh o hm: 14. Tnh o hm ca hm s sau: a) ( ) 2 2 cos2 2+ x x yb) 6 52+ x x yc) ( ) x x x x y sin 2 cos 22+ d) ( )xx xy3cos sin 3 ln +c) ( ) 1 ln2+ + x x y15. 1) Nu ( )xxx f22sin 1cos+th 3434' ,_

,_

f f2) Nu ( )xx f+1 1ln th ( )( ) x fe x f x +1 .'16. Cho ( ) xxx f2cos2 1 Gii phng trnh ( ) ( ) ( ) 0 1' x f x x f17. Cho ( ) ( ) 1 32+ + x x e x fx. Gii phng trnh ( ) ( ) x f x f 2'18. ( ) x x f 2 sin3 v ( ) . 4 sin 5 2 cos 4 x x x g Gii phng trnh ( ) ( ) x g x f '19. Gii bt phng trnh: ( ) ( ) x g x f' '>.vi ( )1 25 .21+xx f v ( ) 5 ln . 4 5 x x gx+ 20. Tnh o hm: a) ( )( ) ( ) 4 223 . 12+ ++x xxyb) x xxxx y2 323 2cos . sin .11.+c) xxy ,_

+ 11. 21. Tnh o hm ti x = 0. ( )' 0 00 ,1cos .2x voix voixxx f y22. a)tm a v b hm s: ( )( )' + +< + 0 10 .2voi bx axx voi e a xx f ybx c o hm ti x = 0. b) Tnh o hm theo nh ngha ca hm s ax y sin c) Tnh o hm cp n ca hm s ax y sin * Tnh gii hn: 23. x xxxsin 2 cos 1lim2024. ( ) 1 sin1lim2 31 +xx xx 25. xxxcos 1cos 1lim0 26. xxxcos 11 2 1lim20+ 27. 211lim+

,_

+xxxx 28.112lim+

,_

+xxxx29. ( )23 2 201 ln1lim2xx exx++ 30. 20cos 3lim2xxxx 31. 14 7 3lim3 3 21 + + +xx xx 32. xx xx308 1 2lim + 33.12 1 2lim5 41 + xx xx* o hm cp cao34. ( )3 220 3 522 x xx xx f y. Tnh ( )( ) x fn35. ( ) x x f y 5 sin2 . Tnh ( )( ) x fnPHIU S 236. Cho hm s: ( ) x a x a a x y ,_

+ + 2 sin43cos sin21312 3 tm a hm s lun ng bin. 37. Cho ( ) ( ) 9 4 12 2 3+ + + x a x a x y tm a hm s lun ng bin.38. Cho ( ) ( ) ( ) 2 8 3 1 1312 3+ + + + a x a x a x a y Tm a hm s lun nghch bin. 39. Cho ( ) ( ) x a x a x y 3 1312 3+ + + Tm a hm s ng bin trn (0;3). 40. Cho hm s ( ) a x a x x y 4 1 32 3+ + + + Tm a hm s nghch bin trn (-1;1)41. Cho hm s ( ) a xx xy+882 Tm a hm s ng bin trn [1;+).42. Cho hm s 1 23 22++ xa x xy. Tm a hm s nghch bin trn (-1/2; +).43. Chng minh rng vi mi x > 0 ta c x x x x < < sin61344. Chng minh rng vi 20 ,< < x x ta c: 123sin 22 2 2+> +xtgx x45. Chng minh rng vi 20 ,< < x xta c :1 sin2 2 2+> +x tgx x46. Chng minh rng vi20 ,< < x x ta c: x tgx >47. Chng minh rng vi20 ,< < x x ta c: 3322 sinx xx1 th 49. Chng minh rng vi x > 0, x 1. Ta c: xx x 11ln > y x. CMR: y xy x y xln ln 2 >+56. CMR: 2211 x x ex+ + > vi mi x > 0. 57. Cho hm s a xa ax xy+ + 2 22 tm a hm s ng bin vi mi x > 1. 58. Cho hm s ( ) ( )312 3 1312 3+ + x m x m mx y. Tm m hm s ng bin [2;+).59. Cho hm s m mx x x y + + + 2 33 tm m hm s ng bin trn mt on c di ng bng 1. B - CC TR HM S60. Tm khong n iu v cc tr ca hm s sau: a) xx y1+ b) 10 36 3 22 3 + x x x yc) 5 3 22 x x yd) 6 2412 4+ x x y e) 16 32+ x x xy61. Cho hm s ( ) 5 3 22 3 + + + mx x x m yTm m hm s c cc i, cc tiu. 62. Cho hm s: ( ) x a x a a x y ,_

+ + 2 sin43cos sin21312 3. Tm a hm s t cc i, cc tiu ti x1, x2 v x12+ x22 = x1+x2. 63. Cho hm s ( ) ( )212 3 1312 3+ + x m x m mx y Tm m hm s t cc tiu ti x1, x2 v x1 + 2x2 = 1. 64. Cho hm s 432+ + xm x xy .Tm m 4 CT CDy y.65. Cho hm s ( ) ( ) 5 32 3+ + + m mx x m x x f y. Tm m hm s t cc tiu ti x = 2. 66. Cho hm s ( ) ( ) 1 1 32 3 + x m mx mx x f yTm m hm s khng c cc tr.67. Cho hm s ( ) ( ) 1 1 3 42 3 4+ + + + x m mx x x f y Tm m hm s ch c cc tiu khng c cc i.68. Cho hm s 182+ +xm mx xy. Tm m hm s c cc i, cc tiu nm v hai pha ng thng 0 1 7 9 y x. 69. Cho hm s 4 2 22 4+ + m mx x y. Tm m hm s c cc i, cc tiu lp thnh tam gic u. 70. Cho hm s 121 2+ x mx y. a. Tm m hm s c cc i, cc tiub. Tm qu tch cc im cc i. PHIU S 4GI TR LN NHT V GI TR NH NHT CA HM SB sung phn cc tr71. Tm khong n iu v cc tr ca hm s sau: a) 2 32 322+ ++ x xx xy b) ( ) 1 ln . 1 + + x x yc) ( ) ( )24 2 . 1 2 x xy d) 2 32sin2cos 3 + x x xy) 62 + x x y f) 432xx xy72. Tm a hm s 1 12 9 22 2 3+ + x a ax x y t cc tr ti x1, x2 v a) 221x x b) 21 12 12 1x xx x+ +* Gi tr ln nhtv nh nht ca hm s 73. Tm gi tr ln nht v nh nht ca hm s: 112++xxy trn on [-1;2]74. Tm gi tr ln nht v gi tr nh nht uca hm s: 24 x x y + 75. 1 xxe y trn [-2;2]76. ( ) 2 log231 + x x y trn [3;6]77. x x x y ln233 22+ + trn 1]1

4 ;2178. Tm gi tr ln nht ca hm s 90 72 32 3+ + + x x x ytrn [-5;5]79. Cho x, y, z thay i tho mn iu kin: x2+y2+ z2 = 1. Tm gi tr ln nht v nh nht ca biu thc: xz yz xy z y x P + + + + + .80. Tm gi tr nh nht ca biu thc z y xz y x P1 1 1+ + + + + . Tho mn: 0 , ,23 + + z y x z y xPHIU S 5GI TR LN NHT V NH NHTTm gi tr ln nht v nh nht ca hm s: 1. x x y3sin 3 3 sin 2. 21cos sin2+ x x y3. x x x y2 2sin 7 sin 3 3 cos 4 + + 4. x x y2cos + trn 1]1

4; 0 .5. x x y 5 cos cos 5 trn 1]1

4;4 6. 1 cos1 cos cos 22++ +xx xy7. x x x x y cos sin 3 cos sin4 4+ + 8. x x x y 3 cos312 cos21cos 1 + + + 9. x x x x y 3 sin912 sin41sin 1 + + + + trn [0;]10. x x yb asin . cos vi 1 , : , :20 > q p N q p x11. x x x x 2 cos 7 3 cos . 2 cos . cos 2 trn 1]1

8;83 12. 11 4cos1 2cos2 2++++xxxxy13. Tm gi tr nh nht ca hm s: x xycos1sin1+ 14. ( ) ( ) x x x x y 8 cos 4 cos214 cos . 2 sin 1 2 + . 15. 8 cos 4 cos 5 cos 2 cos2 2+ + + + x x x x yPHIU S 6TNH LI, LM, IM UN - TIM CN CA TH HM S81. Cho hm s: ( ) 5 3 1 32 3 + x x m x ya. Tm m hm s li mi x (-5;2)b. Tm m th hm s c im un honh x0 tho mn: x0 > m2 2m -582. Tm a v b th hm s: y = ax3 + bx2 c im un a. I (1;-2)b. I (1;3)83. Tm khong li lm v im un ca cc th hm sa. 3b x a y c. 1 25 x yb. xe x y. d. ( ) 231 xxy84. Cho hm s: ( ) m x m mx x y 2 22 3+ + + a. Tm qu tch im un b. Chng minh rng tip tuyn ti im un c h s gc nh nht.85. Chng minh rng th hm s sau c ba im un thng hng. a. 11 22+ ++x xxy b. 2 233a xxy+86. Tm m th hm s: ( ) 1 22322 3 4 + + + m x x m mx y lun lm. 87. Tm m hm s: ( ) 1 2 2 2 22 3 4 + + m mx x x m y li trong khong (-1;0)88. Tm tim cn ca th hm s (nu c)a. ( ) 2 43 +x xxyd. 3 3 23 x x y b. ( ) 2 3 ln2+ x x ye. 5 4 22 ++x xxyc. 4 6 22+ + x x yf. 5 42+ x x y89. Bin lun theo m cc tim cn ca th hm s sau. a.22 62+ +xx mxyb. 2 3122+ x x mxyc. m x xxy+ +4 22PHIU S 7Chuyn : HM S90. Cho hm s 2 32 3 + x x ya. Kho st hm s b. Vit phng trnh tip tuyn vi th hm s ti im unc. Chng minh rng im un l tm i xngd. Bin lun s nghim ca phng trnh sau theo m: 0 32 3 + m x x91. Cho hm s ( ) ( ) x m mx x m y 2 3 1312 3 + + a. Tm m hm s ng bin. b. Tm m hm s ct trc honh ti 3 im phn bit. c. Kho st hm s khi 23 m92. Cho hm s ( ) ( ) 1 12 1 3 3 22 2 3+ + + + x m m x m x ya. Kho st hm s khi m = 0. b. Tm a phng trnh0 2 3 22 3 + a x x c 3 nghim phn bit. c. Tm m hm s c cc i, cc tiu.d. Vit phng trnh ng thng i qua im cc i, cc tiu ca th hm s. 93. Cho hm s 3 72 3+ + + x mx x ya. Kho st hm s khi m = 5. b. Tm m hm s c cc i, cc tiu vit phng trnh ng thng i qua im cc i, cc tiu ca th hm s. c. Tm m trn th c hai imc hai im phn bit i xng nhau qua gc to . 94. Cho hm s 4 92 3+ + + x mx x ya. Kho st hm s khi m = 6. b. Vit phng trnh tip tuyn vi th (C) va v bit tip tuyn qua A(-4;0)c. Tm m trn th hm s c hai im phn bit i xng nhau qua gc to .95. Cho hm s 1 33+ + m mx x ya. Tm m th hm s tip xc vi trc honh.b. Kho st hm s khi m =1.c. Gi th hm s va v l th (C). Vit phng trnh tip tuyn vi (C) bit tip tuyn song song vi x y9196. Cho hm s ( ) 4 3 2 32 2 3+ + + x m m mx x ya. Kho st v v th hm s khi m = 1. b. Gi th va v l th hm s (C). Vit phng trnh parabol i qua im cc i v, im cc tiu ca th hm s (C) v tip xc vi (D). c. Hy xc nh m th hm s cho c im cc i v im cc tiu nm v hai pha ca trc Oy. 97. Cho hm s 3 4 22 3 + x x x ya. Kho st s bin thin v v th ca hm s. Gi l th (C). b. CMR: (C) ct trc Ox ti im A(-3;0). Tm im B xng vi im A qua tm i xng vi th (C).c. Vit phng trnh cc tip tuyn vi (C) i qua im M(-2;5).98. Cho hm s ( ) ( ) 1 2 6 1 3 22 3 + + x m x m x ya. Kho st s bin thin v v th hm s khi m = 2. Gi l th (C). b. Vit phng trnh cc tip tuyn vi (C) bit rng tip tuyn i qua im A(0;-1).Vi gi tr no ca m th (Cm) c cc i v cc tiu tho mn. 2 +CT CDx x99. Cho hm s ( ) 1 33x x y a. Kho s hm s (1). b. CMR: Khi m thay i, ng thng cho bi phng trnh: ( ) 2 1+ + x m yLun ct h hm s (1) ti mt im A c nh. Hy xc nh cc gi tr m ng thng ct th hm s (1) ti ba im A, B, C khc nhau sao cho tip tuyn vi th ti B v C vung gc vi nhau. c. Tm trn ng x = 2 nhng im t c th k ng ba tip tuyn n th (C)100. Cho hm s ( ) C x x y 2 32 3 + a. Kho st s bin thin v v th hm s cho. b. Tm cc im thuc th hm s (C) m qua k c mt v ch mt tip tuyn ti th hm s (C).101. Cho hm s 2 32 3+ + x x y (C)a. Kho st s bin thin v v th ca hm s (C)b. Tm trn trc honh nhng im m t k c ba tip tuyn ti th ca hm s (C).102. Cho hm s 1 9 62 3 + x x x y (C).a. Kho st s bin thin ca hm s. b. T mt im bt k trn ng thng x = 2 ta c th k c bao nhiu tip tuyn ti th ca hm s (C). PHIU S 8Chuyn hm s103. Cho hm s: ( )mC m x m x x y + + 2 2 33a. Kho st khi m = 0. b. Tm m hm s c cc i, cc tiu i xng nhau qua ng thng (D) c phng trnh 2521 x y104. Cho hm s: 12 3 + m mx x ya. Vit phng trnh tip tuyn ti cc im c nh m hm s i qua vi mi m. b. Tm qu tch giao im cc tip tuyn khi m thay i. c. Kho st hm s khi m = 3. d. Gi th hm s va v l (C). Hy xc nh cc gi tr ca a cc im cc i v cc tiu ca (C) v hai pha khc nhau ca ng trn (Pha trong v pha ngoi) 0 1 5 4 22 2 2 + + a ay x y x105. Cho hm s m mx x y + 2 323(Cm)a) Tm m hm s c im cc i, cc tiu nm v hai pha ng phn gic gc phn t th nht. b) Vi m = 1. Kho st v v (C). Vit phng trnh parabol i qua im cc i, cc tiu ca (C) v tip xc vi (D): x y21106. Cho hm s: ( ) 2 1 32 3+ + m mx x ya.CMR: m hm s c cc tr.b. Tm m hm s t cc tiu ti x =2. c. Kho st vi m va tm c.d. Gi th va v l th hm s (C). Trn h trc to khc t th hm s (C) suy ra th hm s (C) ca hm s ( ) 1 2 22 x x x ye. Bin lun theo k s nghim ca phng trnh: 12 22 xkx x107. Cho hm s: 2 33+ x x y(C)a. Kho st v v th hm s. b. Vit phng trnh tip tuyn ti im x0 =1. Ca th hm s (C).c. Trn h trc to khc t th (C) suy ra th (C) ca hm s ( ) 2 32+ x x yd, Tm m phng trnh ( ) 0 32 m x x c bn nghim phn bit. 108. Cho hm s: 1 32 3+ + x x ya. Kho st hm s.b. ng thng i qua A(-3;1) v c h s gc l k. Xc nh k ng thng ct (C) ti 3 im phn bit. c. Bin lun theo m s nghim ca phng trnh. 0 1 1 3 32 3 + + m t t c bn nghim phn bit. 109. Cho hm s: 6 32 3 x x ya. Kho st hm sb. Bin lun s nghim ca phng trnh. m x x 6 32 3110. Cho hm s: ( ) ( ) 1 2 3 1 32 3+ + x m m x m mx ya. Kho st hm s khi m = 0.b. Vi gi tr no th hm s ng bin trn tp gi tr x sao cho: 2 1 x111. Cho hm s: ( ) 1 1 32 3 + x m mx mx ya. Cho m =1. Kho st hm s Vit phng trnh tip tuyn ca th hm s bit tip tuyn qua A(1;-1).b. Vi gi tr no ca m th hm s c cc tr v mt cc tr thuc gc phn t th nht, mt gc cc tr thuc phn t th 3.PHIU S 9HM S112. Cho hm s:( ) ( ) ( ) 1 4 1 4 2 1 32 2 3+ + + + + m x m m x m x y (1) (m l tham s)1. Chng minh rng khi m thay i, th (1) lun i qua im c nh. 2. Tm m sao cho (Cm) ct trc honh ti 3 im phn bit.113. Cho hm s: ( ) ( ) x a ax x a y 2 3 1312 3 + + 1. Tm a hm sa. Lun ng bin. b. C th ct trc honh ti 3 im phn bit.2. Kho st s bin thin v v th vi 23 a3. T th suy ra th hm s x x x y2523612 3+ + 114. Cho hm s: ( ) m x x x x f y + + 9 32 31. Kho st khi m = 6. 2. Tm m phng trnh f(x) = 0 c ba nghim phn bit. 115. 1. Kho st s bin thin v v th ca hm s ( ) 1 33+ x x x f y2. Tm a th ca hm s ( ) x f y ct th hm s ( ) ( ) a ax x a x g y + 3 32 ti ba im c honh dng.116. Cho hm s ( ) ( ) 1 1 3 32 2 2 3 + m x m mx x y (Cm)1. Vi m = 0. a. Kho st s bin thin ca hm s (C0)b. Vit phng trnh tip tuyn (C0) bit tip tuyn qua M(1 ;32)2. Tm m (Cm) ct trc 0x ti ba im phn bit honh dng.117. Cho hm s ( )3 2 2 31 3 3 m x m mx x y + a. Kho st khi m = 2. b. Tm m (Cm) ct Ox ti 3 im phn bit trong c ng hai im c honh m. 118. Cho hm s: ( ) x x m x y 9 1 22 3 + 1. Kho st s bin thin ca hm s khi m = 1. 2. Tm m th ct Ox ti ba im phn bit lp cp s cng.119. Cho hm s: m x x x y + 9 32 31. Kho st hm s khi m = 0.2. Tm m th hm s ct Ox ti ba im phn bit c honh lp cp s cng.120. Cho hm s: m x mx x y + 3 42 31. Chng minh rng vi mi m hm s lun c cc i, cc tiu tri du. 2. Kho st hm s khi m = 0.3. Phng trnh 2 31 3 4 x x x c bao nhiu nghim.121. Cho hm s: 1312 3+ + m x mx x y1. Khi m = 0a. Kho st hm sb. Cho A(0;0), B(3;7). Tm M thuc AB ca (C) sao cho din tch MAB ln nht.2. Chng minh vi mi m hm s lun c cc i, cc tiu. Tm m khong cch gia im cc i, cc tiu l nh nht. 3. Tm m im un ca th hm s l

,_

31; 1 E122. Cho hm s: ( ) mx x m x y + + + 2 33 41. Xc nh m hm s nghch bin trn (0;3).2. Kho st hm s khi m = 9. 3. Tm m 1 y khi 1 x123. Cho hm s: ( )3 2 2 2 31 3 3 a a x a ax x y + + 1. Khi a = 1. a. Kho st hm s.b. Tm m phng trnh: 2323 m x x c bn nghim phn bit. 2. Tm a hm s y ng bin vi [ ] [ ] 2 ; 0 1 ; 3 x124. Cho hm s: ( ) ax x x f y 31. Khi a = 3. a. Kho st hm s.b. Vit phng trnh parabol i qua A(( ) 0 ; 3 ), B(0 ; 3) v tip xc vi th va v.2. Vi gi tr no ca x th tn ti t x sao cho f(x) = f(t). PHIU S 10HM S125. a. Cho hm s ( ) 131 3+xxy kho st hm sb. Tm mt hm s m th ca n i xng vi th ca hm s (1) qua ng thng x + y -3 = 0c. Gi (C) l mt im bt k trn th hm s (1). Tip tuyn vi th hm s (1) ti C ct tim cn ng v ngang ti A v B. Chng minh rng: C l trung im AB v tam giac to bi tip tuyn vi hai tim cn c din tch khng i. 126. Cho hm s ( )m xm x my++ +1 (1)1-Vi m =1. a. Kho st hm s. b. Gi s th hm s va v l (H). Tm trn (H) nhng im c tng khong cch n hai ng tim cn l nh nht. 2- Tm a sao cho phng trnh: att++1 sin1 sin 2c ng hai nghim tho mn iu kin t 03-Chng minh rng vi mi m th ca hm s (1) lun lun tip xc vi mt ng thng c nh. 127. Cho hm s ) (2 2mCm xm mx xy + a. Kho st hm s vi m =1. b. Tm m (Cm) c cc i, cc tiu. Lp phng trnh ng thng i qua hai im cc i, cc tiu.c. Tm cc im trn mt phng to c ng hai ng (Cm) i qua. 128. Cho hm s: 112+ xx xy (C)a. Kho st hm sb. Tm m (Dm): 1 mx y ct (C) ti hai im phn bit m c hai im thuc cng mt nhnh. c. Tm qu tch trung im I ca MN. 129. Cho hm s: 11 2 32+ + +xm mx mxy1-Cho 21 ma. Kho st hm s. b. Bin lun theo k s nghim ca phng trnh: 0 1 2 32 + + x k x x2-Tm m th hm s c im cc i, cc tiu nm v hai pha i vi trc Ox.130. Tm cc ng tim cn nu c ca th hm s sau:a. ( ) 2 3 ln2+ x x yb. 12xxyc. 3 42+ x xxyd. 22+ xe ye. 92+x xyf. x x x y 2 32 + + g. 2 32+ x x yh. 4122++ xxx yPHIU S 11HM S131. Cho hm s: ) (23 32Cxx xy++ +d. Kho st hm s (C). e. Vit phng trnh tip tuyn vi (C) bit tip tuyn vung gc vi ng thng (d): 3y x + 6 = 0. f. Bin lun theo tham s m s nghim [ ] ; 0 t ca phng trnh: ( ) 0 2 3 cos 3 cos2 + + m t m t132. Cho hm s: ( )122+ + +xm x m xyd. Xc nh m tim cn xin ca (Cm) h trn hai trc to mt tam gic c din tch bng 12,5.e. Kho st hm s khi m = 4. f. Xc nh k ng thng y = k ct th (C) va v ti hai im phn bit E, F sao cho on EF l ngn nht. 133. Cho hm s: ( )12 3 12+ + + xm x m xyd. Kho st hm s khi m = 1. e. Tm nhng im M thuc th hm s va v sao cho to ca M l cc s nguyn. f. Tm m hm s c cc i, cc tiu ng thi gi tr cc i, cc tiu cng du. 134. Cho hm s: ) (11 22mCxm mx mxy+ + +d. Tm m th (Cm) c c tim cn ng v tim cn xin. e. Tm m th (Cm) c cc i, cc tiu nm phn t th nht v th ba. Ca mt phng (Oxy). f. Tm m th (Cm) ct trc Ox ti hai im phn bit. Tm h s gc ca tip tuyn vi th ti cc im . 135. Cho hm s: m x mx xy +82d. Kho st hm skhi m = 6. e. Tm m hm s c cc tr. Khi hy vit phng trnh ng thng i qua im cc i, cc tiu. f. Xc nh m th ct trc honh ti hai im phn bit v tip tuyn ti hai im vung gc vi nhau. PHIU S 12HM S136. Cho hm s: ( )m xm x m xy+ + +1 12 (1)4. Kho st hm s khi m = 1. 5. Chng minh rng vi mi m - 1, th ca hm s (1) lun tip xc vi mt ng thng c nh, ti mt im c nh. 6. Tm m hm s ng bin trn ( ) + ; 1137. Cho hm s: ( )) 1 (1 1 22m xm x m xy + + +4. Kho st hm s khi m = 1. 5. Tm m hm s nghch bin trong khong ( ) + ; 26. Chng minh rng vi mi m - 1, cc ng cong (1) lun tip xc vi mt ng thng c nh ti mt im c nh. 138. 1. Kho st hm s: 1 22+ x x xy2. Trn h trc to khc t th hm s (C) suy ra th hm s (C) ca hm s: 1 22+ x x xy3. Bin lun theo a s nghim ca phng trnh: ( ) 1 22+ + + x a a x139. Cho hm s: ) (15 52Cx x xy+ 4. Kho st hm s: 5. Trn h trc to khc t th hm s (C) suy ra th hm s (C): 15 52+ x x xy6. Tm m phng trnh: ( ) 1 2 5 2 . 5 4 + t t tm c bn nghim phn bit. 140. Cho hm s: 13 32++ +x x xy3. Kho st hm s (C).4. Tm hai im A, B trn hai nhnh khc nhau ca (C) sao cho di on AB ngn nht. 141. Cho hm s: 21 sin 2 cos .2+ +xx x xy (a l tham s)5. Kho st hm s khi a6. Tm hai im A, B trn hai nhnh khc nhau ca (C) sao cho di on AB ngn nht. 7. Tm a hm s c tim cn xin. 8. Tm a hm s c hai cc tr tri du. PHIU S 13HM S142. Cho hm s: ( )m xm x m xy+ + +1 12(C)1. Kho st hm s khi m = 2. 2. Chng minh rng: tch cc khong cch t mt im tu thuc (C) n hai ng tim cn khng i.3. Tm m hm s c cc i, cc tiu v gi tr cc i, cc tiu tri du. 143. Cho hm s: 12+ xm mx xy1. Kho st hm s khi m = 1. 2. Chng minh rng vi mi m hm s lun c cc tr v khong cch gia cc im cc tr l khng i. 144. Cho hm s: 22+xxy1. Kho st s bit thin ca hm s. 2. Tm trn th nhng im cch u hai trc to . 3. Vit phng trnh tip tuyn ca th bit tip tuyn i qua A(-6,5).145. Cho hm s: 11+xxy (H)1. Chng minh rng cc ng thng y = x + 2 v y = - x l trc i xng. 2. Tm M thuc (H) c tng khong cch n cc trc to l nh nht. 146. Cho hm s: 232xxy (H)1. Kho st s bin thin v v (H). 2. Tm M thuc (H) sao cho tng khong cch t M n hai trc to l nh nht. 147. Cho hm s: ) (25 42Hxx xy++ +1. Kho st s bin thin v v th ca hm s. 2. Tm M thuc (H) sao cho khong cch t M n (D): 0 6 3 + + y x nh nht. 148. Cho hm s: 11+xxy1. Kho st s bin thin ca hm s. 2. Chng minh rng mi tip tuyn ca th u lp vi hai ng tim cn mt tam gic c din tch khng i. 3. Tm tt c cc im thuc th sao cho tip tuyn ti lp vi hai ng tim cn mt tam gic c chu vi nh nht. PHIU S 14HM S154. Cho hm s: 23212 4+ mx x y1. Khi m = 3.a. Kho st s bin thin ca hm s.b. Vit phng trnh tip tuyn i qua A

,_

23; 0 ca th trn. 2. Tm m hm s c cc tiu m khng c cc i. 155. Cho hm s: ( ) m x m mx y 2 1 12 4 + + 1. Tm m hm s ch c mt cc tr2. Kho st s bin thin ca hm s khi 21 m3. Vit phng trnh tip tuyn ca th bit tip tuyn qua O(0;0). 156. Cho hm s: ( ) 3 1 22 2 4 + m x m x y (Cm).1. Xc nh m (Cm) khng c im chung vi trc honh. 2. Vi gi tr no ca m th hm s t cc tr ti x = 1. Kho st s bin thin v v th ca hm s vi m = 1. 3. Bin lun s nghim ca phng trnh( ) k x x 22 2 theo k. 157. Cho hm s: ( ) 1 2 1 22 4 + + m x m x y1. Tm m hm s ct trc Ox ti 4 im c honh lp cp s cng. 2. Gi (C) l th khi m = 0. Tm tt c nhng im thuc trc tung sao cho t c th k c ba tip tuyn ti th. 3. Tm m sao cho th (C) chn trn ng thng y = m ti ba on thng c di bng nhau. 159. 1. Kho st hm s: 1 22 4 x x y2. Tm tt c cc gi tr ca m sao cho phng trnh sau c su nghim phn bit. m x x22 4log 1 2 160. Cho hm s: ( ) 9 10 62 4+ + + x m x y1. Kho st hm s khi m = 0. 2. CMR: mi m khc 0, th hm s cho lun ct trc Ox ti 4 im phn bit, chng minh rng trong s cc giao im c hai im nm trong khong (-3;3) v c hai im nm ngoi khong . 161. Cho hm s: ( ) ( ) 2 21 1 + x x y1. Kho st hm s. 2. Bin lun theo m s nghim ca phng trnh: ( ) 0 1 2 1 22 + m x3. Tm b parabol b x y + 22 tip xc vi th v phn 1. PHIU S 15HM S162. Cho hm s: ( )21 2xxy (C)1. Kho st hm s. 2. Hy xc nh hm s y = g(x) sao cho th ca n i xng vi th (C) qua A(1;1). 163. Cho hm s: ( ) C x x y 12 4+ 1. Kho st hm s. 2. Tm nhng im thuc Oy t k c ba tip tuyn ti th (C)164. Cho hm s: 1 12+ x x xy1. Kho st hm s. 2. Tm trn trc Oy nhng im t c th k c hai tip tuyn ti th va v. 165. Cho hm s: 12+xxy 1. Kho st hm s 2. Cho A(0;a). Xc nh a t A k c hai tip tuyn n (C) sao cho hai tip im tng ng nm v hai pha i vi Ox. 166. Cho hm s: ) (11Cxxy+1. Kho st hm s. 2. Tm nhng im thuc Oy m t mi im y ch k c ng mt tip tuyn ti (C). 167. Cho hm s: 111+ + xx y1. Kho st hm s: 2. Bin lun theo m s nghim ca phng trnh: 1cos1sin1cot21cos sin ,_

+ + + + + mx xgx tgx x x vi

,_

2; 0 xPHIU BI TP S 16.Cho A(2;-1), B(0;3), C(4;2). Tm to im D bit rng: D l im i xng ca A qua B. 0 4 3 2 + CD BD ADABCD l hnh bnh hnh ABCD l hnh thang c cnh y AB v D Ox. Cho ABC tm chn ng phn gic trong AD v tm ng trn ni tip ABCTm trn trc honh im P sao cho tng khong cch t P n A(1;2) v B(3;4) t gi tr nh nht.Trn mt phng to cho tam gic c mt cnh c trung im l M(-1;1), cn hai cnh kia c phng trnh l x + y 2 = 0 v 2x + 6y + 3 = 0. Xc nh to cc nh ca tam gic. Cho tam gic ABC c nh A(2,2). Lp phng trnh cc cnh ca tam gic bit ng cao k t B v C ln lt l: 9x 3y 4 = 0 v x + 2y = 2. Vit phng trnh cc ng trung trc ca tam gic ABC, bit trung im cc cnh l M (-1;-1), N (1;9), P(9;1).Cho P(3;0) v hai ng thng (d1): 2x y 2 = 0; (d2): x + y + 3 = 0. Gi (d) l ng thng qua P v ct (d1), (d2) ln lt A v B. Vit phng trnh ca (d) bit rng PA = PB. Lp phng trnh cc cnh ca tam gic ABC nu cho A (1;3) v hai ng trung tuyn c phng trnh ln lt l: x 2y + 1 = 0 v y 1 = 0. Cho tam gic ABC c nh B (3;5) v ng cao AH c phng trnh: 2x 5y + 3 = 0. Trung tuyn CM c phng trnh: x + y 5 = 0. Vit phng trnh cc cnh ca tam gic ABC. Lp phng trnh cnh ca tam gic ABC bit B (2;-1) v ng cao AH c phng trnh: 3x 4y + 27 = 0 v phn gic trong CD c phng trnh: x + 2y 5 = 0. Cho tam gic ABC c nh A (2;-1) v phng trnh hai ng phn gic gc B v gc C l: x 2y + 1 = 0 v x + y + 3 = 0. Vit phng trnh ng thng cha cnh BC. Cho A(-6;-3), B(-4;3), C(9,2). Vit phng trnh ng phn gic trong (d) ca gc A trong ABCTm P (d) sao cho ABCP l hnh thang.Cho (d1): 2x y 2 = 0; (d2): 2x + 4y 7 = 0. Vit phng trnh ng phn gic trong to bi (d1) v (d2).Vit phng trnh ng thng qua P (3;1) cng vi (d1), (d2) to thnh mt tam gic cn c nh l giao im ca (d1) v (d2). Cho (d1) c phng trnh: '+ t yt x22 1 v (d2) c phng trnh:'+ t yt x23 3Vit phng trnh ng phn gic gc t to bi (d1) v (d2).Vit phng trnh ng thng i qua giao im ca hai ng thng (d1): 3x 5y + 2 = 0; (d2): 5x - 2y + 4 = 0 v song song vi ng thng (d): 2x y + 4 = 0. Cho P (2;5) v Q(5;1). Vit phng trnh ng thng qua P v cch Q mt on c di bng 3. Vit phng trnh ng thng i qua im A(0;1) v to vi ng thng x + 2y + 3 = 0 mt gc 450. Vit phng trnh cc cnh ca hnh vung, bit rng hnh vung c nh l (-4;8) v mt ng cho c phng trnh l 7x y + 8 = 0. Cho A(1;1). Hy tm im B trn ng thng y = 3 v im C trn trc honh sao cho tam gic ABC u. Cho (d1) x + y 1 = 0, (d2) x 3y + 3 = 0. Vit phng trnh ng thng (d3) i xng vi (d1) qua (d2). PHIU S 17PHNG TRNH NG THNG PHNG TRNH NG TRNTrong mt phng Oxy cho tam gic ABC bit A(3;7), B(9,5) v C(-5;9). Vit phng trnh ng phn gic trong gc ln nht ca tam gic ABC.Qua M(-2;-7) vit phng trnh ng thng tip xc vi ng trn ngoi tip tam gic ABC. Cho tam gic ABC, 3 cnh c phng trnh l: 0 4 : + y x AB; 0 5 2 : + y x BC; 0 40 8 : + y x CATnh di ng cao AH. CMR: G BAC nhn. Vit phng trnh ng phn gic trong gc A.Vit phng trnh tng qut ca ng thng qua I(-2;3) v cch u hai im A(5;-1) v B(0;4).Cho A (3;0) v B(0;4), C(1;3) vit phng trnh ng trn ngoi tip v ni tip tam gic ABC Cho A(5;-3); B(-3;-4), C(-4;3). Vit phng trnh ng trn ngoi tip tam gic. Vit phng trnh ng trn qua A(4;2) v tip xc vi hai ng thng (D1), 0 2 3 y x (D2): 0 18 3 + y xVit phng trnh ng trn c tm nm trn ng thng x = 5 v tip xc vi hai ng thng: 0 3 3 + y x v 0 9 3 + y x. Vit phng trnh ng trn i qua im A(1;2) v B(2;1) v c tm nm trn ng thng 0 1 3 7 + +y x. Vit phng trnh ng trn tip xc vi ng thng 3x 4y 31 = 0 ti A(1;-7) v c bn knh bng 5. Vit phng trnh ng trn i qua im A(1;2) v i qua giao im ca ng thng x 7y + 10 = 0 v ng trn 0 20 4 22 2 + + y x y xCho ng trn tm (C) c phng trnh: 0 6 6 22 2 + + y x y x v im M(2;4). Vit phng trnh ng thng (d) i qua M v ct (C) ti hai im A, B sao cho M l trung im AB. Vit phng trnh tip tuyn ca C bit tip tuyn song song vi ng phn gic phn t th t v phn t th hai.Vit phng trnh ng trn (C) i xng vi ng trn (C) qua im M.Cho A(-2;0), B(0;4)Vit phng trnh ng trn i qua im O, A, B. (O l gc to ).Vit phng trnh tip tuyn vi (C) ti A v B. Vit phng trnh tip tuyn vi (C) bit tip tuyn qua M(4;7).Vit phng trnh ng thng i qua gc to O(0;0) v ct ng trn (C) c phng trnh 0 15 6 22 2 + + + y x y x. To thnh mt dy cung c di bng 8.ng thng (D): 2x y 1 = 0. Ct (C) 0 1 2 42 2 + + y x y x ti M v N tnh di M, N. Cho (C) 0 1 4 22 2 + + y x y x qua A(0;1) k hai tip tuyn vi (C), cc tip im T1T2 a) Vit phng trnh ng thng T1T2 b)T nh d i T1T2. 36) Cho hai ng trn: ( ) 0 4 4 2 :2 21 + + y x y x C ( ) 0 14 2 2 :2 22 + + y x y x Ca. Chng minh rng hai ng trn trn ct nhau ti A v B. b. Vit phng trnh ng thng i qua hai im A, B. c. Vit phng trnh ng trn i qua hai im A, B v im M (0;1).37. Cho (Cm) c phng trnh: ( ) 0 1 2 22 2 + + my x m y xa) Tm m Cm l ng trnb) Tm qu tch tm ca Cm.c) CMR: khi m thay i, cc ng trn (Cm) lun i qua mt im c nh.d) Cho m = -2 v im A(0;-1). Vit phng trnh cc tip tuyn ca ng trn (C) k t A.38. Cho (Cm): 0 2 42 2 + + + + m y mx y xa) Tm im M (Cm) l ng trn b) Tm im c nh ca (Cm).c) Khi (Cm) i qua gc to O(0;0). Hy vit phng trnh t() song song vi (D) c phng trnh 3x + 4y + 2006 = 0. V() chn trnn ng trn mt on c di bng 1.d) Tm m (Cm) tip xc vi Oy. PHIU S 18N TP NG THNG - NG TRN (tip)39. Cho ng trn (C) c phng trnh: 0 21 8 62 2 + + y x y x v A(4;5), B(5;1)a)CMR: Trong hai im A, B c mt im nm trong ng trn, mt im nm ngoi ng trn. b) ng thng AB ct (C) ti E v F. Tnh di EF. c) Tm cc gi tr ca m hai im M(m;m-1) v N(m-1;m) cng thuc min trong ca ng trn (C). 40. ng trn (C1) c bn knh R1 = 1. V tm I1 thuc phn dng ca trc Ox. ng thi tip xc vi trc Oy. ng trn (C2) c bn knh R2 v tm I2 thuc phn m ca trc Ox ng thi tip xc vi trc Oy. a) Vit phng trnh (C1), (C2).b)Xc nh to giao im ca tip tuyn chung ngoi v trc honh. c) Vit phng trnh tip tuyn chung ca (C1), (C2). 41. (C): 0 12 2 + y x ;( ) ( ) 0 5 4 1 2 :2 2 + + + y x m y x Cma) Tm qu tch tm (Cm). b) CMR: c hai ng trn (Cm) tip xc vi (C). c) Vit phng trnh tip tuyn chung ca hai ng trn (Cm) . 42. ( ) 0 4 2 4 :2 2 + + m y mx y x Cma) Tm m (Cm) l ng trn.b) Tm qu tch tm ng trn.c) CMR: Cc ng trn (Cm)lun tip xc vi nhau ti mt im c nh.43. CMR: H ng thng (Dm): ( ) 0 2 2 1 22 + m y m mx lun tip xc vi mt ng trn c nh.44. CMR: h ng thng (Dm) c phng trnh: ( ) ( ) 68 8 4 5 32+ + + + m m y m x m lun tip xc vi mt ng trn c nh. 45. Cho h ng trn: ( ) ( ) 0 1 2 1 2 2 :2 2 + + + m y m mx y x Cm.a) Chng minh rng khi m thay i (Cm) lun i qua hai im c nh.b) CMR: m , h ng trn lun ct trc tung ti hai im phn bit. PHIU S 1946.1. Xc nh di hai trc, to cac nh tiu c, tm sai, to tiu im, khong cch 2 ng chun, bn knh qua tiu v phng trnh hnh ch nht c s ca (E) sau: a. 20 5 42 2 + y xb. 0 64 42 2 + y xc 0 11 16 18 4 92 2 + + y x y xd. 1 64 92 2 + y x2. Vit phng trnh chnh tc ca (E) bit: a. Hai nh trn mt trc l: A(0;-2), B(0;2) v mt tiu im F(1;0). b. Tm O, trc nh trn Oy, tiu c bng tm sai bng 53c. Tm O, mt nh trn trc ln l (5;0) v phng trnh ng trn ngoi tip hnh ch nht c s l: 412 2 + y x47. Tm nhng im trn (E) 1922 + yxa. C bn knh qua tiu im ny bng ba ln bn knh qua tiu im kia. b. To vi hai tiu im mt gc 900. c. To vi hai tiu im mt gc 120o. 48. Chng minh tch cc khong cch t cc tiu im ti mt tip tuyn bt k ca (E) bng bnh phng di na trc nh. 49. Cho (E): 0 40 42 2 + y xa. Xc nh tiu im, hai nh trn trc ln, hai nh trn trc nh v tm sai ca (E). b. Vit phng trnh tip tuyn vi (E) ti Mo(-2;3). c. Vit phng trnh tip tuyn vi (E) bit n xut pht t cc im M(8;0). Tnh to tip im. d. Vit phng trnh tip tuyn vi (E) bit n vung gc vi ng thng (D): 0 1 3 2 + y x. Tnh to tip im. 50. Vit phng trnh (E): 12222 +byax, nhn cc ng thng 0 20 2 3 y x v 0 20 6 + y x lm tip tuyn. 51.a. Vit phng trnh ca (E) c tiu c bng 8, tm sai 54 e v cc tiu im nm trn Ox i xng nhau qua Oy. b. Vit phng trnh cc tip tuyn ca (E) i qua

,_

415; 0 M52. Vit phng trnh tip tuyn chung ca hai elp: 116 252 2 + y x v 125 162 2 + y x53. Trong mt phng to cho hai (E) c phng trnh: 11 162 2 + y x v 14 92 2 + y xa. Vit phng trnh ng trn i qua giao im ca hai elp. b. Vit phng trnh tip tuyn chung ca hai elp. 54. Cho (E): 13 62 2 + y x. Xt mt hnh vung ngoi tip (E) (tc l cc cnh hnh vung ngoi tip E). Vit phng trnh cc ng thng cha cnh ca hnh vung . 55. Cho (E): 36 9 42 2 + y x v tip im M(1;1). Vit phng trnh ng thng qua M v ct (E) ti hai im M1, M2 sao cho MM1=MM2. 56. (E): 0 12222> > + b abyaxa. Chng minh rng vi mi im ( ) E M ta u c a OM b . b. Gi A l mt giao im ca ng thng kx y vi (E). Tnh OA theo a, b, k.c. Gi A, B l hai im thuc (E) sao cho OB OA CMR: 2 21 1OB OA+ khng i. 57. Trong mt phng to cho (E): 14 92 2 + y x v hai ng thng ( ) 0 : by ax D ( ) ( ) 0 0 :2 2 '> + + b a ay bx Da. Xc nh cc giao im M, N ca (D) vi (E) v cc giao im P, Q ca (D) vi (E). b. Tnh theo a, b din tch t gic MPNQ. c. Tm iu kin i vi a. b din tch ln nht. d. Tm iu kin i vi a, b din tch y nh nht. 58. Cho (E). 14 92 2 + y x A(-3;0), M(-3;a), B(3;0), N(3;b) vi a, b thay i. a. Xc nh to giao im I ca AN v BM. b. CMR: ng thng MN tip xc (E), iu kin cn v ca a, b l ab = 4.c. Vi a, b thay i sao cho MN lun tip xc vi (E). Hy tm qu tch im I. PHIU S 20ELP HYPEBOL59. Cho (E): 64 16 42 2 + y x1. Xc nh F1 ,F2, tm sai v v Elip.2. M l mt im bt k trn (E).Chng minh rng: T s khong cch t M ti F2 v ti ng thng 38 x c gi tr khng i. 3. Cho ng trn (C): 0 4 3 42 2 + + x y x Xt ng trn (C) chuyn ng nhng lun i qua tiu im phi F2 v tip xc ngoi vi (C). Chng minh rng tm N ca (C) thuc mt hypebol c nh (H). Vit phng trnh (H). 60. Cho (E): 116 252 2 + y x1. Xc nh k v m (D): m kx y + tip xc vi (E).2. Khi (D) l tip tuyn ca (E), Gi giao im ca (D) vi (D1): x =5; (D2): x = -5. ln lt ti M v N. Tnh din tch tam gic FMN theo m, k vi F l tiu im c honh dng. 3. Tm k din tch tam gic FMN t gi tr nh nht. 61. Cho (E): 1422 + yx v ng trn (C) c phng trnh: 0 3 42 2 + + y y x1. Vit phng trnh tip tuyn ca (C) bit tip tuyn qua A(2;0).2. Vit phng trnh tip tuyn chung ca (E) v (C). 3. Cho M l mt im chuyn ng trn ng thng x =4. Gi MT1 v MT2 l hai tip tuyn ca (E ) xut pht t M (vi T1 ,T2 l hai tip im). Chng minh rng trung im I ca T1T2 chy trn mt ng trn c nh. Vit phng trnh ca Elp . 62. Cho (H): 4 42 2 y x1. Xc nh tiu im, nh, tm sai v cc ng tim cn ca (H). 2. Vit phng trnh tip tuyn vi (H) bit tip tuyn i qua N(1;4). Tm to tip im. 63. Cho (H): 144 16 92 2 y x1. Tm im M trn (H) sao cho hai bn qua tiu im ca M vung gc vi nhau.2. Vit phng trnh ca (E) c cc tiu im trng vi cc tiu im ca hypebol v ngoi tip hnh ch nht c s ca hypebol. 3. Vit phng trnh cc tip tuyn ca (H) i qua cc nh ca (E) nm trn trc Oy. 64. Cho (H): 116 252 2 y xGi s M l im bt k thuc (H). Chng minh rng. Din tch ca hnh hnh xc nh bi hai ng tim cn ca (H) v hai ng thng i qua M v tng ng song song vi hai tim cn , khng ph thuc vo v tr im M. 65. Cho (E): 0 192 24 82 2 + y x5. Xc nh to tiu im, tm sai v cc nh ca (E).6. Vit phng trnh tip tuyn () vi (E) v tm to tip im bit () song song vi ng thng: x + y = 1975.7. Tm ( ) E G bit GF1 = 3GF2 vi F1, F2 ln lt l tiu im bn tri v bn phi ca (E).8. Cho N(2;4). T N k hai tip tuyn NH1 v NH2 ti (E) vi H1, H2 l hai tip im. Vit phng trnh H1H2.65. Cho (E) c phng trnh: 0 136 17 82 2 + y x 5. Xc nh to tiu im v tm sai v cc nh ca (E).Vit phng trnh tip tuyn ca () vi (E) bit() song song vi ng thng: x y = 2003. 7. Tm ( ) E G bit 2 13 F GF G vi 2 1, F F ln lt l cc tiu im bn tri v bn phi ca (E).8. Cho N(1;4) t N k hai tip tuyn MH1 v NH2 ti (E) vi H1, H2 l hai tip im. Vit phng trnh H1 H2.67. Cho (E): 225 25 92 2 + y x5. Vit phng trnh chnh tc v xc nh cc tiu im, tm sai ca (E)? 6. Mt ng trn (C) c tm I(0;1) v i quaim A(4;2). Vit phng trnh ca (C) v chng minh (C) i qua hai tiu im ca (E).7. ng thng (d1) c phng trnh y = kx ct (E) ti M v P, ng thng (d2) xky1 ct (E) ti N v Q (th t MNPQtheo chiu kim ng h). Chng minh rng: MNPQ l hnh thoi v 2 21 1ON OM+ khng i.8. Tm k din tch MNPQ nh nht.68. 1. Vit phng trnh chnh tc ca (H) bit tm sai 313 e, tiu c bng 3 22. ( ) H M . Gi F2 l tiu im ca (H) c honh dng. Chng minh rng t s khong cch t M n F2 v n ng thng 139 x khng i.3. Tip tuyn vi (H) ti M acts hai tim cn ti A v B. Chng minh rng: din tch tam gic OAB khng i. 69. Cho (H). 0 80 3 52 2 y x5. Xc nh to tiu im, cc nh tm sai v hai ng tim cn ca (H).6. Vit phng trnh tip tuyn () vi (H) v tm to tip im bit tip tuyn () song song vi ng thng 200223+ x y.7. Tm ( ) H M bit MF1 = 2MF2 vi F1, F2 ln lt l tiu im bn tri v bn phi ca (H). 8. Cho N(1;2). T N k hai tip tuyn NK1 v NK2 ti (H) vi K1 v K2 l hai tip im. Vit phng trnh K1 K2. PHIU S 21Chuyn : NGUYN HMTm nguyn hm ca hm s sau. 1. ( )311 3++xxy2. x xy313. x xxy3424. 6 5 1 22+ x xxy5. 8 14 76 22 32 + + +x x xx xy6. ( ) 3211+ +xx xy 7. ( ) ( ) 3 1132+ +x xxy 8. ( )321 xxy9. 5 62 4+ +x xxy10. 2 33 3 332+ + +x xx xy11. Tm nguyn hm ca hm s f(x) khi bit. f(x) = x x 3 cos . 5 cos v 14 ,_

G12. Tm nguyn hm ca hm s f(x) bit. ( )4 4 cos4 cos158 sin .22+xxex ex f v 08 ,_

GTm cc nguyn hm sau: 13. x x x y 4 cos . 2 cos . cos 14. x x 8 sin . cos315. x g tgxx xy2 cot 4 sin . 3 sin+16. ( ) ( ) x x x x y6 6 4 4cos sin . cos sin + + 17. xysin118. xycos 11+19. x xycos 3 sin 5 31+ +20. 4 5 3cos . sin1x xy 21. x tg y422. x g y3cot 23. xxy42sincos24. xx xy2 cossin sin3+25. x y3sin 26. 1 cos 4 cos23xxyQuang Thoi Chng trnh luyn thi cao ng i hc 2004- 2005PHIU S 22NGUYN HM27. x xxysin sin cos23+28. 33cos cossinx xxy 29. x x y3 2sin . 30.x x y2cos . 31. x e yx4 sin .3 32. x e yx3 cos .233. xxeey221 34. 2.3 xe x y 35. ( )21 ln . x x y + 36. x xyln .1 37. ( ) x y ln cos 38. x y sin 39. x xxycos sin sin+ 40. x xxysin coscos+41. 3cos sincos sinx xx xy+42. 1 2 1 21 + ++ x xtgx y43. 1 31+ + +x xy44. 101 +xxy45. 3 21 x y + 46. 3 231 xxy+47. x x y 1 .4 48. 32 31++xxy49. 1 .3 2+ x x y50. 112 x xy51. x xx xycos sin 3cos 2 sin++52. x xycos sin 21 +53.

,_

+4cos . cos1x xy54. xxy2 sin 1 sin+55. ( ) 2ln . x x y 56. ( ) x e yx2sin . 57. ( ) x x xyln ln . ln .1 58. x xxyln 1ln+PHIU S 23VC T KHNG GIANBi 1: Cho t din ABCD: 1. Chng minh rng: Nu CD AB , BD AC th BC AD 2. Tm im O sao cho: 0 + + + OD OC OB OA (*)3. Chng minh im O tho mn h thc (*) l duy nht. (t ny cn thiu)Quang Thoi Chng trnh luyn thi cao ng i hc 2004- 2005PHIU S 24TCH PHN59. xdx os c4060. +202 cos 2cosdxxx61. 202 2cos . sinx xdx62. 244sinxdx63. +203cos 1sin 4xxdx64. +20cos sin sindxx xx65. +36cos sin cosdxx xx66. +202 sin 2sin cosdxxx x67. +02cos 2sindxxx x68. +02cos 4 9sindxxx x69. + 202 sin 1 dx x70. +202 cosxdx71. +202 2 2 2sin . cos .cos . sindxx b x ax x72. ++242 sin 3sin cosdxxx x73. ++202 2cos 4 sin 3cos 4 sin 3dxx xx x74. ++ +26cos sin2 cos 2 sin 1dxx xx x75. ( )+ +4032 cos sin2 cosdxx xx(NT:00) 76. +402cos 3 sin cosdxx xx77. 3622 cos 12 cosdxxx78. 203cos cosdx x x79.80. +0cos 1 dx xQuang Thoi Chng trnh luyn thi cao ng i hc 2004- 2005PHIU S 25TCH PHN81. +1021xxedx e82. +1031dxeexx83. +2 ln0 11dxeexx84. +102 x xe e dx85. +2 ln05xe dx86. +edxxx1ln 187.( )+ +1021 ln dx x x x88. ( )edx x x12ln(PVBC:98)89.( )+edxxx121ln90.a( )edx x1ln sin90. ( ) dx x os celn1(SGK) 91. ( )+1022 dx e x xx92. 20. 2 cos .dx x ex93. ( )+211 ln dx x94. ( ) dx x ex202sin95. 21ln xdx x96. +30cossindxx x x97. ( )+2121 lndxxx98. ( )+ +2221 ln . cosdx x x x99. +2 ln021 dxeexx100. Quang Thoi Chng trnh luyn thi cao ng i hc 2004- 2005PHIU S 26TCH PHN101. + + +101 3 x xdx102. + + +012 4 x xdx103. ( )++370 32 3 1dxx dx x(GT:89) 104. +302 51 dx x x105. 102 21 dx x x106. 202 24 dx x x107. 220221 xdx x108. 101 dx x x109. ++221211dxx xx110. +203 21dx x x111. +102 31 dx x x112. +101 2xxdx113. +4729 x xdx114. 23221 x xdx115. +108 153 1 dx x x116. + +10231 x xdx x117. +1031 x xdx118. ( )10321 dx x119. +402cos 14 sinxxdx120. ( )+203cos sinsin 4dxx xx121. +206 66cos sin sindxx xx122. +401tgxdx123.a ( )3203sindx x (KT:01) 123.b.20sindx x(SGK)124.

,_

+ ++2 ln0222 3 3dxe ee ex xx x125. ++20cos 1sin 1dx exxxQuang Thoi Chng trnh luyn thi cao ng i hc 2004- 2005PHIU S 27N TP TCH PHN126. ( )dxx xxIx

,_

++++ 9101231 411 2 sin5(GT:)127. +106411dxxx128. + +102 43 4x xxdx129. dxx xx x x+ ++ + +1022 39 21 10 2130. 3462cossindxxx131. +362 22 cotdx x g x tg(M: 00 )132. +dxxx1 3sin2133. +01 sin xdx134. +401tgxdx135. 2333 3cotsinsin singxdxxx x(HVKTQS:97)136. ( )xedx x1. ln cos137. ( )+112. sin2dx x e x ex x138. Tm a, b hm s ( ) 22+ + xbxax f tho mn iu kin. a421' ,_

fv( ) 1212 ln 3 2 dx x f139. Tm a, b hm s ( ) ( ) b x a x f sin tho mn iu kin. ( ) 2 1' f v ( )204 dx x f140. CMR: Nu hm s f l hm s chn v lin tc trn R: R x v 0 > a ta c( )( ) +xxxtdt t f dxat f01(BK:99)141. Cho hm s f lin tc trn [ ] 1 ; 0CMR: ( ) ( ) 2020cos sin dx x f dx x f142. Cho hm s f lin tc trn [ ] 1 ; 0CMR: ( ) ( ) 0 0sin2sin dx x f dx x xf143. Cho hm s f lin tc v ( ) ( ) x f x b a f +.CMR: ( ) ( ) +babadx x fb adx x xf2Quang Thoi Chng trnh luyn thi cao ng i hc 2004- 2005PHIU S 28DIN TCH HNH PHNG* Tnh din tch hnh phng gii hn bi cc ng. 144. 1 sin sin2+ + x x y, 0 y, 0 x v 2 x.145. x x y2ln . ; trc Ox; x = 1; x = e. 146. xe y ; xe y, 1 x.147. x x y 22 , x x y 42+ .148. 3 42+ x x y; 3 y.149. ( ) 5 4 :2+ x x y P. V 2 tip tuyn ca (P) ti 2 im A(1;2) v B(4;5).150. Trn mt phng to tiu chun cho 2 ng Parabol: 22 3 8 x x y v 22 9 2 x x y + .1. Xc nh a v b sao cho ng thng b ax y + ng thi l tip tuyn ca parabol. Xc inh to ca cc tip im. 2. Tnh din tch hnh phng gii hn bi hai ng parabol cho v tip tuyn va xc nh trn. 151. (P): x y 22. Chia hnh phng gii hn bi ng trn: 82 2 + y x thnh 2 phn tnh din tch mi phn. 152. Tnh din tch hnh phng gii hn bi cc ng: 0 22 + x y y v 0 + y x.153. Tnh din tch hnh phng gii hn bi cc ng 0 13 + y x; 0 1 + y x; 0 y.154. Tnh din tch hnh phng gii hn bi cc ng x y ; 22 x y .155. Tnh din tch hnh phng gii hn bi cc ng 6 42 3+ + x x x y v trc Ox. Quang Thoi Chng trnh luyn thi cao ng i hc 2004- 2005PHIU S 29HON V - CHNH HP - T HP1. Rt gn: a. ( ) ( ) 6 845 6 + n n nA A AMnn nb. ( )( ) 31 2112++ +nA n PPANnnnnnn2. Gii phng trnh: a. n An203b. ( ) 15 2 52 3+ + n A An n3. Gii bt phng trnh: ( ) ( )! 115! 24