IV §1 nh ngh a: ) a g i p c a ng hi u: a  A, n u a  A h ng ng c ng thay cho t nh to n  ua th a g i p thi u c a  u a>A th a g i p th a c a : A   thi  a  3.14 p thi u c a  A   thi  a  3.15 p th a c a  ) t i: a nh ngh a: t i c a p ac a ng là:  Aa  a  A b nh ngh a: t i c a p ac a ng  a cho   A  a   a  a   a  A  a   a : m t i giới h n  a c a p a c a ng  : 3.14    3.15  a    0.01   a  0.01 3) t ng i:  l  158.6cm  0.1cm o chi u ài tr c   l2  5.4cm  0.1cm ặc ph p o c c ng t i giới h n h ng r ràng ph p o l t t h n l2 nh ngh a: t ng i giới h n c a p a hi u:  a c c nh:   a  a   a   a a  A  a1   a  a : t u §2 I c h i ni 1) nh l : àm y ( ) liên t c a, b & f a  f b  đo x0  a, b nghi m c a ph ng tr nh ( ) inh h a h nh au: y y  f x  f b  a x0 b x f a  : h ng minh r ng pt: x3  x   lu n c : t nh t nghi m x  0;1 t f x   x  x  liên t c 0;1 & f 0 f 1  1   x0  0,1 nghi m c a pt ) m ho ng c l p nghi m: t pt f x   0, a; b g i ho ng c l p nghi m c a pt n u n th a c c i u i n au: 1) f a  f b   x0  a; blà nghi m c a pt 2) f x  h ng i u a; b  c a; b  hàm ch t ng gi m  pt f x   c uy nh t nghi m a; b  3) f x  h ng i u a; b  c a; b  hàm h ng c i m u n ta nhanh ch ng t m c nghi m ngày ch nh c hư ng ph p c ng y Bb, f b  y  f x  a  x0 x1 Aa, f a  x2 x3  x b A1 x A2 ) t ài to n: Cho pt: f x   01 hàm ( ) i u iễn ây cung a; b nghi m c a pt ( ) giao i m c a ng cong ới o g i x  nh ng ta th t m ch nh mà ch c th t m c c c nghi m p ới x  1, x2, x3 rong x3 lần l t c c giao i m c a ây cung ,A1B, A2B ới ox i ho ng (a ) hàm ( ) th a i u i n ta c : h ng tr nh ây cung  a  x0 y  f a  xa  with  f b   f a  b  a d b  x  x0 y  f a   f d   f  x0  d  a AB  ox   x1 ,0  x1  x0  nh n c nghi m ch nh d  x0  f x0  f d   f  x0  c h n ta lặp l i u tr nh i ới x1; band we have : x2  x1  d  x1  f x1  f d   f x1  hi y x0 , x1, x2 , ti n ần n nghi m ng c a pt ( ) : m nghi m gần ng c a pt: f(x) = x3- 6x + c x 1, x2, : f 0 f 1  6   n0 , x0  0;1 f   x  0, x  0;1with x0   f  x0   f 1  3  f  f  x0    d  0 1 f 1  0.4 f 0  f 1 f  x1   f 0.4  0.336  0, f 0   x2  0;0.4 0.4 x2  0.4  f 0.4  0.3424 f 0  f 0.4 f  x2   f 0.3424   0.014  0, xet 0, x2 , d  x1    0.3424 f 0.3424   0.34 f 0  f 0.4 hư ng ph p ti p t n t n x3  0.3424  y Aa, f a  a  x0 x1 x2 x y  f x  b x Bb, f b  i a ho ng c l p nghi m c a pt: ( ) rong a ng i ta thay ng cong ng ti p n c a n t i a ti p n c t o t i  x1 ta xem x1 nghi m gần ng c a x i ch n x0  a, PTTT at Ax0 , f x0  : y  f x0   f x0 x  x0  f x0  i p n c t o t i x1,0   f x0   f x0 x1  x0   x1  x0  f x0  t m nghi m ch nh c h n n a ta l p l i u tr nh ới i m x1, f x1  ta f  x1  thu c nghi m theo c ng th c: x2  x1  f x1  n c n l i ới ng ng cong ( ) th ta ch n a hay a t c c h nh au: y y B x a x1 A x  A y  f x  b x x a x1 x y  f x   f  x     f a   cho x0  a  y  f x  A x  f  x   B f a   cho x0  a  y y a b x A B x1 b x x y  f x  x x x1 b a B  f  x     f b   cho x0  b  m l i: f x  gi nguyên i n: f x  f x0   : x  f  x     f b   cho x0  b  u x  a; b , ta cho x0 a hay n u n th a i u  m nghi m gần ng c a ph ng tr nh: x3  x   tre n 0;1 ng ph ng ph p ti p n: : Coi f  x   x  x  f 0  2, f 1  3, f  x   x  0, x  0;1  f  x  f 0   cho x0  a  f  x0  0  0.33 f  x0  6 f 0.33  0.0559   f  x  f 0.33   thay Ta co : x1  x0  x0 bă ng f  x1  0.0559 Ta co : x2  x1   0.33   0.33985 f  x1   5.6733 x1 :  m nghi m gần ng c a ph ng tr nh: x3  0.2 x  0.2 x  1.2  tre n ng ph ng ph p ti p n: : 1.1;1.4 Coi f  x   x  0.2 x  0.2 x  1.2 f 1.1  0.331, f 1.4  0.872, f  x   x  0.4  0, x  1.1;1.4  f  x  f 1.4   cho x0  b  1.4 f  x0  0.872  1.4   1.22969 f  x0  5.12 f  x1   f 1.22969   0.1111   f  x  f 1.22969    thay f  x1  0.1111 Ta co : x2  x1   1.22969   1.20079 f  x1  3.8445 Ta co : x1  x0  x0 bă ng x1 hư ng ph p ph i h p i (a ) ho ng c l p nghi m c a ph ng tr nh ( ) p ng ng th i ph ng ph p: ây cung cho nghi m gần ng ti p n cho nghi m gần ng x1 h x1, x1 n m ph a c a nghi m o ho ng c l p nghi m thu h p nhanh h n i p t c p ng ph i h p cho x1, x1 ta c ho ng c l p nghi m x2 , x2 i p t c cho n hi ta c   xk , xk sao hi  cho xk  xk   a nghi m gần ( cho ph p) x  xk ng là: xk  k y y  f x  a x1 x2 x x2 x1 B b x A nh minh h a cho ph ng ph p ph i h p:  : ng ph ng ph p ti p n t nh nghi m gần  1) x3  x   tre n 2,3 2) x  x treˆn 0;0.5 nh n ng c a ph ớc lặp th  3) x5  5x   tre n  1,0 ch nh c n  4) x  x   tre n 1,2 nh n ớc lặp th ng tr nh: ... x0  5 . 12 f  x1   f 1. 22 969   0 .11 11   f  x  f 1. 22 969    thay f  x1  0 .11 11 Ta co : x2  x1   1. 22 969   1. 20 079 f  x1  3. 844 5 Ta co : x1  x0  x0 bă ng x1 hư ng... 1. 1 ;1 .4 Coi f  x   x  0 .2 x  0 .2 x  1. 2 f 1. 1  0.3 31, f 1 .4  0.8 72, f  x   x  0 .4  0, x  1. 1 ;1 .4  f  x  f 1 .4   cho x0  b  1 .4 f  x0  0.8 72  1 .4   1. 22 969... 0, f 0   x2  0;0 .4 0 .4 x2  0 .4  f 0 .4  0. 3 42 4 f 0  f 0 .4 f  x2   f 0. 3 42 4   0.0 14  0, xet 0, x2 , d  x1    0. 3 42 4 f 0. 3 42 4   0. 34 f 0  f 0 .4 hư ng ph p