giới hạn của hàm số

          n n − +           n n n n − − = + +             n n − − = = = + +          !"#"$#%&  !"#"$#%&    !  ! x x "#$%&'$()*+, "#$%&'$()*+, x x   ( ( x x   → →   x x x x 1 1 = = … … - - → →   f(x) f(x) f(x f(x 1 1 ) ) f(x f(x 2 2 ) ) f(x f(x 3 3 ) ) f(x f(x 4 4 ) ) … … f(x f(x n n ) ) - - → → . .  ,  ,   x x f x x − = −    x =    x =  /  x =  n n x n + =  01   ,   n n n f x x n + = = 2  ,  n f x    2 324'5 6 ,x n (x n 73 x n 8( 9:f(x) 'x;<    ,   n n f x n + = 01324 '5 6 ,x n (x n 73x n 8( f(x n )8          n n + + = = =  ,   ,    n n n n x x f x x − = −  < <  n n x x= = = =  ,    ,    n n n n n x x n f x x x n − + = = = − =>?@?A@BC,DA9 =>?@?A@BC,DA9 EF<0G< EF<0G<   @:GH$:&%I @:GH$:&%I   JKL JKL AMN, AMN, x x n n 24'OP 24'OP x x n n 7 7 3 3 x x n n → → ' ' →+ →+ ∞ ∞       ,  x x f x L → =  Q , ,      n n n n n x x x x x − + − = − −  Q ,   x f x x − = −   ,  x f x →  ,  n f x =   ,  R x f x → = E) ,    R n x= + = + = 0GST    @:GH$:&%I @:GH$:&%I   JKUL JKUL AMN, AMN, x x n n 24'OP 24'OP x x n n 7 7 U3 U3 x x n n → → U' U' n→+ n→+ ∞ ∞   , U U U R n x= + = + =  R ,  U x f x x − = − U  ,  x f x →  R , U, U   U U n n n n n x x x x x − + − = − −  ,  n f x = E) U  ,  R x f x → =  !"#'()*$+#,"# #,"  !"#'()*$+#,"# #," =& =& AMN3<9: AMN3<9: 2?!V 2?!V f(x) f(x) W W 3(5 3(5 L L W W 3 3 ?)H,c X     Y  x x x x x x c c → → = = !VM7   ,  x x f x L → =   ,  x x g x M → =   Z ,  , [ x x f x g x L M → + = +   Z ,  , [ x x f x g x L M → − = −   Z , < , [ < x x f x g x L M → =   ,  x x f x L → =  ,   ,  x x f x L g x M → =   ,  x x f x L → = EF<  0G  20G    ,  x f x →   ,    x f x x − = −    ,   x x g x x − + = −   ,  x g x →    2     ,     ,     ,  x x x x x x f x x x → → → → − − = = − −   <  <   <  <  x x x x → → − − = = = − −       ,    x x x x g x x → → − + = −  , ,    x x x x → − − = −   ,       x x x x → → = − = − = − = − MTcsofx 5\1x  /0x12 @\x 1 324x 2 3 E)x  /0x1235x/65x/26 ?3 0G  ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]] ?3 0G   AM ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]] AM   , ,   ,   x x x x x x → → − + = = + −       x x → = + = + =     ,    ,  <  x x x x x x x x → → → → − − = = + +    <  / − − = = +  ,    x f x x − = +   ,  x f x →     ,     x x x f x x → → − = +     ,   x x g x x − − = −   ,  x g x →      ,    x x x x g x x → → − − = − =>?@?A@BC =>?@?A@BC ^0G ^0G y = y =   f(x) f(x) H$:&%I'GM, H$:&%I'GM, x x o o Y Y b b < <   L L :_`a :_`a gii hn bên phi gii hn bên phi   y = f(x) y = f(x) ' ' x x → → x x 0 0 !V !V 3, 3, x x n n 24'5( 24'5( x x 0 0 < x < x n n <b <b 3 3 x x n n → → x x 0 0 ( ( f(x f(x n n ) ) → → L L < < 9\V 9\V 2 +#,"789:;"   ,  x x f x L + → = ^0Gy =f(x)H$:&%I'GM,a ; x o < L:_`agii hn bên tri y = f(x)'x → x 0 !V 3,x n 24'5(a<x n bx 0 3x n → x 0 (f(x n ) → L< 9\V   ,  x x f x L − → = x 0 b x  x x + → x 0 a x  x x − → =>?@cd =>?@cd   '3e' '3e'   ,  x x f x L → =    ,   ,  x x x x f x f x L − + → → = = EV0G 3 2,@G:+$:&a:ff(x) xg     ,  x f x + →   ,  x f x − →   ,   b ax x f x x x + ≥  =  −  !V !V    ,  ,     x x f x x − − → → = − = − = −    ,  ,   x x f x ax a + + → → = + = +    ,   ,     x x f x f x a a − + → → = ⇔ + = − ⇔ = − 2=ff(x)x =5 [...]... = L →x 0 0 Hướng dẫn bài tập về nhà x2 − 4x + 3 1) Tính lim x →3 x −3 2) Xác định a để hàm sô f(x) có giới hạn tại x = 2  x 2 + 1 nêu x ≥ 2 f ( x) =  1 − ax nêu x < 2 BT: Cho hàm sô lim a) Tính x → 2− f ( x)  x + 8 nêu x ≥ 2 f ( x) =  ax + 1 nêu x < 2 lim f ( x) x → 2+ b) Xác định a để hàm sô f(x) có giới hạn tại x = 1