1. August 16 ,2009 http://my.opera.com/vinhbinhpro Nhn space bar hay click chut xem cc dng v trang k tip Bin tp PPS : vinhbinhpro

2. Phn VII Kho st v v th ca hm hu thttp://my.opera.com/vinhbinhpro http:my.opera.com/vinhbinhpro 3. Tm tt gio khoa vinhbinhproaxb Kho st v v th hm s : y(c0 ; ad bc 0)cxd d * Tp xc nh :D Rc adbc * Chiu bin thin ca hm sy' 2cx d1. ad - bc > 0 => y > 0 , x D => Hm s lun ng bin trn tx D 2. ad - bc < 0 => y < 0 ,x D => Hm s lun nghch bin trn tx D( c hai trng hp hm s khng c cc tr )* Gii hn v ng tim cn :d lim y; lim yx l tim cn ng dd xx c ccaaa lim y; lim yyl tim cn ngang xc xcc 4. vinhbinhpro Tm tt gio khoad lim y; lim y x l tim cn ng dd xx c cc aa a lim y ; lim yy l tim cn ngang x cx c c * Bng bin thin : 5. vinhbinhpro Tm tt gio khoadlimy; lim yxl tim cn ngd dx x cc c aaalim y; lim y yl tim cn ngangxcx cc * Bng bin thin : ad - bc > 0ad - bc < 0d dx- c +x- c+ y ++y - -+aa+ yycca ac- -c* Giao im ca 2 ng tim cn l tm i xng ca th. 6. Tm tt gio khoatim cn ng x=-d/c y ytim cn ngang y = a/c tim cn ngang y= a/c 0 x0 xtim cn ng x=-d/ctm i xng tm i xng ad - bc >0 ad - bc < 0 bin tp pps: vinhbinhpro 7. Tm tt gio khoa 2ax bxc( t khng chia Kho st v v th hm s : y (a 0;a' 0)ht mu ) a'xb' b' * Tp xc nh : D Ra' * Chiu bin thin ca hm s : c th tnh y theo cc cch sau2 2 ax bx c aa'x2b ' a xbb' a 'c 1. y y' 2a'x b' a'xb'Q a 'Q 2. Ly t chia mu : ykx ly'k2a'xb'a'x b'( kx +l l THNG v Q l s D trong php chia t cho mu)2 Ax Bx C Tng qut : 2 y'y'0AxBx C0 (* ) 2 a'xb'Du ca y ph thuc vo s nghim ca phng trnh (*) v A = a.a vinhbinhpro 8. Tm tt gio khoa * Gii hn v ng tim cn :b' lim y lim yx l tim cn ng b' b'a' x x a' a'QQ ykx l ;lim y kx l lim 0a'x b' xx a'xb'=> y = kx + l l tim cn xin ca th hm s* Chiu bin thin : vinhbinhpro 9. Tm tt gio khoa * Chiu bin thin :x 1. Trng hp 1 : y ' 0Ax 2 Bx C 0 Click vo xem tipx 2. Trng hp 2 : y ' = 0 V NGHIM Click vo xem tipLc ny du y lun cng du vi A = a a vinhbinhpro 10. vinhbinhproTm tt gio khoa* Gii hn v ng tim cn :b' lim y lim y x l tim cn ng b'b' a' x x a'a' Q Q ykx l ; limy kxllim 0 a'xb'x xa'x b'=> y = kx + l l tim cn xin ca th hm s* Bng bin thin : x 1. Trng hp 1 : y'0Ax 2 BxC 0 xA = a a > 0 A = a a < 0 b' b'x-a' +x- a'+ y + 0 --0 + y - 0++0 -+ ++ +y CCctyct-- - - 11. Tm tt gio khoahttp://my.opera.com/vinhbinhproCh : Cch tnh gi tr cc trGi x il im cc tru ( xi )Ngoi cch tnh :y ( xi ) ta cn c cch tnh sau : v ( xi )u '( x i ) y ( xi )(vi u l o hm ca t u(x) v v l o hm ca mu v(x)v '( x i ) ) * th :a) th hm s l mt hyperbol khng vung gc b) Giao im ca 2 ng tim cn l tm i xng ca thCch dng :1. Dng 2 ng tim cn2. Dng im cc i v cc tiu ca th hm s3.Dng 2 nhnh ca th ( i qua cc im c bit) 12. Tm tt gio khoavinhbinhpro A= a a > 0 hay k > 0 A= a a < 0 hay k < 0yy im cc tiutm i xng tm i xng xx 00 tim cn ng x = - b/aim cc itr v 13. Tm tt gio khoa * 2. Trng hp 2 : y ' = 0V NGHIMLc ny du y lun cng du vi A = a a A = a a > 0A = a a < 0 b'b'x-a'+x- a'+ y+ +y- - + + ++ y y - --- 2 2 a x a xlim ylim lim ylimxx a'x xxa'x 2 a x a x 2lim ylim lim ylimxx a'x xxa'x http://my.opera.com/vinhbinhpro 14. Tm tt gio khoa *A = a a > 0 hay k > 0 A = a a < 0 hay k < 0y yx= - b/atm i xng0x 0 x tr v vinhbinhpro 15. vinhbinhpro Bi tp 1m 2 x m 2 Cho hm s : y (m 1; m2) xma) nh m 2 ng tim cn ca th ct nhau trn ng thng y = 2x - 5b)Kho st v v th hm s khi m = 3 Hng dn : a) lim m 2 x m 2 m2 m 2 0 m1 ;m 2x m lim y xm l tim cn ngx mm 2x m 2x lim ylimm 2 => y = m - 2 l tc ngangx x m x 1x Giao im ca 2 ng tim cn l im I (m ; m - 2 ) I d : y 2x5 m2 2m5 m 3 16. Bi tp 1* x 1 b) m3 ; y x 3* Tp xc nh : D R 3 4y' 2 0 x D Hm s nghch bin trn tng khong xc nhx3lim y; lim y => x = 3 l tim cn ngx3 x 3xlim ylim 1 ; lim y 1 => y = 1 l tim cn ngangxx x x * Bng bin thin http://my.opera.com/vinhbinhpro 17. Bi tp 1*x 1 b) m3 ; yx 3* Tp xc nh :D R 34y' 20 x D Hm s nghch bin trn tng khong xc nh x 3lim y ; lim y => x = 3 l tim cn ngx3x 3xlim ylim1 ; lim y1=> y = 1 l tim cn ngangxx xx * Bng bin thin * th :-3+x im c bit :y- -x 0 12 1 + y - 1/3 -2 -3y 1 -http://my.opera.com/vinhbinhpro 18. Bi tp 1**f(x)f(x)=(x+1)/(x-3)f(x)=1x(t)=3 , y(t)=t 4Series 12 x -4 -2 24 6Tm i xng -2 -4 http://my.opera.com/vinhbinhpro 19. Bi tp 2 2 Kho st v v th hm s :x3x 6 y x 1 Hng dn :* Tp xc nh : D R1* Chiu bin thin 2 x* Gii hn v tim cn : lim y lim ; lim y x x x x2 x3x6 lim y lim ; lim y => x = 1 l tim cn ng x1x 1x 1x 1 4 4 y x 2; lim yx 2 lim 0 => y = x - 2 l tim cn ngang x1 xx x 1* Bng bin thin : 2 x 2x 32x1 y'2; y' 0x2x 30 x1x 3 vinhbinhpro 20. Bi tp 2*x--1 13+y +0 - - 0++ +yC ct- - 2 xCD3 yCD y ( 1) 5 im cc i ( - 1 ; - 5 ) 1 2 x ct 3 y ct y (3)3im cc tiu ( 3 ; 3 ) 1 * th : + Giao im 2 ng tim cn I ( 1 ; - 1 ) l tm i xng ca th + Tnh thm ta cc im c bit 21. f(x)f(x)=(x^2-3*x+6)/(X-1)x(t)=1 , y(t)=t 6f(x)=x-2Series 1 4 3 2 x -4 -3 -2 -1 1234-2-4 tm i xngI (1 ; -1 )-5 -6http://my.opera.com/vinhbinhpro 22. Bi tp 32Kho st v v th hm s :x 2x1yx 1Hng dn : * Tp xc nh : D R1* Chiu bin thin2x* Gii hn v tim cn : lim y lim ; lim yx x xx 2x 2x 1lim y lim ; lim y => x = 1 l tim cn ngx 1 x 1 x1x 12 2 y x1 ; lim y x 1 lim 0 => y = - x +1 l tim cn ngangx 1xx x 12x 2x3 * Bng bin thin : y '2; Pt : y '0 VN y' 0; x1x 1Hm s nghch bin trn cc khong ca D v khng c cc trvinhbinhpro 23. Bi tp 2* x- 1 + y - -+ + y - -* th :+ Giao im 2 ng tim cn I ( 1 ; 0 ) l tm i xng ca th+ Tnh thm ta cc im c bit- th ct trc Oy ti im ( 0 ; - 1 ) - th ct trc Ox ti 2 im :12 ;0 ; 1 2 ;0 24. f(x) f(x)=(-x^2+2*x+1)/(x-1)x(t)=1 , y(t)=tf(x)=-x+142 x -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5-2-4 25. * th ca hm s c du gi tr tuyt i Bi ton thng gp : Bit th ( C ) ca hm s y = f( x ) , suy ra th ca :C 1 : y1fxC2 : y2f x a) V th : C 1 : y1f x y1 f x l hm s chn nn th C 1nhn trc Oy lm trc i xngx 0 x x y1f ( x)y(C1 ) (C ) x 0 : thC1l phn i xng ca ( C ) vi x0 qua trc Oy b) V th : C 2 : y 2fx f (x) y ; f (x)0 y2 f (x)f (x) y; f ( x) 0 th hm sC2 : y2f x gm 2 phn :1. Nu f ( x )0 y2y(C 2 ) (C )http://my.opera.com/vinhbinhpro 26. * th ca hm s c du gi tr tuyt i * 2. Nuf ( x) 0 y2y Lc ny th C 2 i xng vi th (C) qua trc Ox( ch ly phn ca (C) ng vi xD1 D vi f ( x ) 0) Bi tp p dng :2x 3x a) Kho st v v th ( C ) ca hm syx 1 b) T th ( C ) suy ra th ( H ) ca hm s : x x 3y x 1Hng dn : (tm tt )a)* Tp xc nh :D R1 2x 2x3 x 1 y 1y'2y' 0x 1 x 3 y 9 27. * th ca hm s c du gi tr tuyt i **x --1 13+y +0-- 0+++y 19- - f(x) f(x)=(x^2+3*x)/(x-1)(C) x(t)=1 , y(t)=t10f(x)=x+4 86tim cn xin y = x+4 42 tim cn ng x=1x-8 -6-4 -22 46 8 (C)-2 http://my.opera.com/vinhbinhpro 28. * th ca hm s c du gi tr tuyt i *b) V th ( H )2 x x3 x 3xx0x x : y1 y (C ) (H )x 1 x 1 2x x 3x 3x x0 xx : y1 yx 1x 1Vy ( H ) i xng vi ( C ) qua trc Ox 29. * th ca hm s c du gi tr tuyt i ** f(x) (C) f(x)=(x^2+3*x)/(x-1) (H) trng (C) vi x0x(t)=1 , y(t)=t10f(x)=x+4 864(H) 2(C) 0 x-8 -6 -4 -2 2 46 8 (H)-2(H) trng (C) vi x 0(C) vinhbinhpro