Bài 1: Giới hạn dạng 0/0 - Khóa LTðH ñảm bảo – Thầy Phan huy Khải Hocmai.vn – Ngôi trường chung của học trò Việt 1 BTVN BÀI GIỚI HẠN DẠNG 0/0 Tính các giới hạn sau ñây: ( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) x 0 x 0 x 0 x 0 x 0 m n x 1 m 1 m 2 x 1 1 x 1 2x 1 3x 1 *Bµi1: lim x 1 x 1 2x 1 3x 1 x 1 2x 1 x 1 2x 1 x 1 x 1 lim x 1 x 1 2x 1 3x 1 1 x 1 2x 1 x lim x 3x 1 x 1 2x 2x 1 x x 3 1 x 1 2x 2 1 x 1 lim lim 1 2 3 6 x 1 x 1 *Bµi 2 : lim x 1 x 1 x x lim → → → → → → − − → + + + − + + + − + + + + + − + + + − = + + + − + + + − + = + + + + + + + + + + = = = + + = − − − + + = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) m 1 m 2 n 1 n 2 n 1 n 2 x 1 100 50 x 1 100 99 98 50 49 48 x 1 x 1 x 1 x x x 1 m lim n x 1 x x x 1 x x x 1 x 2x 1 *Bµi3: lim x 2x 1 x 1 2(x 1) x 1 x x x 1 2 98 49 lim lim 48 24 x 1 2(x 1) x 1 x x x 1 2 − − − − − − → → → → + + + + + + = = − + + + + + + + + − + − + − − − − + + + + − = = = = − − − − + + + + − ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 20 2 10 x 2 3 20 20 20 10 20 20 20 10 10 20 10 x 2 x 2 x 2 2 2 x 0 x 0 x 0 x x 2 *Bµi 4 : lim x 12x 16 x 2 (x 1) x 2 (x 1) x 2 (x 1) 3 lim lim lim (x 2) (x 4) 2 (x 2) (x 4) (x 2) (x 4) x 9 x 16 7 *Bµi 5 : lim x x 9 3 x 16 4 x lim lim lim x x x 9 3 → → → → → → → − − − + − + − + − + = = = = − + − + − + + + + − + − + + − = = + + + ( ) ( ) ( ) x 0 x 0 x 0 x x x 16 4 1 1 1 1 7 lim lim 6 8 24 x 9 3 x 16 4 → → → + + = + = + = + + + + Bài 1: Giới hạn dạng 0/0 - Khóa LTðH ñảm bảo – Thầy Phan huy Khải Page 2 of 3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 x 0 3 3 x 0 x 0 x 0 x 0 x 0 2 3 3 3 2 x 0 3 2 2 x 0 x 0 2 1 x 8 x *Bµi 6 : lim x 2 1 x 1 8 x 2 2 1 x 1 8 x 2 lim lim lim x x x 2x x 1 13 lim lim 1 12 12 x 1 x 1 x 8 x 2 8 x 4 2x 1 1 3x *Bµi 7 : lim x 2x 1 (x 1) 1 3x (x 1) 2x 1 (x 1) lim lim x x → → → → → → → → → + − − + − − − − + − − − = = − − = − = + = + + − + − + + − + + − + − + − + + − + = = ( ) ( ) ( ) ( ) ( ) 2 3 2 2 x 0 x 0 2 2 2 3 3 2 x 0 2 2 2 3 3 3 4 5 x 0 3 x 0 2x 1 (x 1) 1 3x (x 1) x lim lim x 2x 1 (x 1) x 1 3x (x 1) 1 3x (x 1) x (x 3) 1 3 lim 1 2 2 x 1 3x (x 1) 1 3x (x 1) 1 4x. 1 6x. 1 8x. 1 10x 1 *Bµi 8 : lim x 1 4x. 1 6x. 1 8x lim → → → → → + + + + − + − − = + + + + + + + + + − + − = − − = − + + + + + + = + + + + − + + + ( ) ( ) ( ) 4 5 3 4 3 4 3 3 x 0 3 4 5 3 4 x 0 x 0 3 x 0 x 0 2 x 0 . 1 10x 1 4x. 1 6x. 1 8x x 1 4x. 1 6x. 1 8x 1 4x. 1 6x. 1 4x. 1 6x 1 4x 1 4x 1 lim x 1 4x. 1 6x. 1 8x. 1 10x 1 1 4x. 1 6x. 1 8x 1 lim lim x x 1 4x 1 6x 1 1 4x 1 lim lim x x 1 4x 1 XÐt : I lim li x → → → → → → + − + + + + + + − + + + + + − + + + − + + + + + − + + + − = + + + − + − + + + − = = ( ) x 0 n n 5 4 3 2 x 0 4x 4 m 2 2 x 1 4x 1 1 2nx 1 Còng nh− vËy ta cã : I lim 2 I I I I I 8 x → → = = + + + − = = ⇒ = + + + = Bài 1: Giới hạn dạng 0/0 - Khóa LTðH ñảm bảo – Thầy Phan huy Khải Page 3 of 3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 2 x 0 3 3 2 2 x 0 x 0 x 0 x 0 x 0 2 2 2 2 3 3 3 4 x 7 4 4 4 t 2 2x 1 x 1 *Bµi 9 : lim sin x 2x 1 1 x 1 1 x 1 1 2x 1 1 lim lim lim sin x sin x sin x 2 x lim lim 2 0 2 sin x sin x 2x 1 1 x 1 x 1 1 x x x 2 x 20 *Bµi10 : lim x 9 2 t § Æt t x 9 x t 9 I lim → → → → → → → → + − + + − − + − + − + − = = − = − = − = + + + + + + + − + + − = + ⇒ = − ⇒ = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 4 3 4 4 4 t 2 t 2 t 2 4 2 4 t 2 t 2 4 2 3 4 4 3 2 t 2 2 3 4 4 3 3 x 0 7 t 11 t 2 t 7 3 t 11 3 t 16 lim lim lim t 2 t 2 t 2 t 7 3 t 4 t 2 t 16 lim lim t 7 3 t 2 t 11 3 t 11 9 t 4 t 2 16 32 176 lim 3 27 27 t 11 3 t 11 9 1 4x 1 6x *Bµi11: lim → → → → → → → − − + − − − + − − = − = − − − − + + + − − = − + − + + + + + + − = + = + + + + + − + ( ) ( ) ( ) ( ) 2 2 3 2 2 2 x 0 x 0 x 0 3 2 2 x 0 x 0 2 2 2 3 3 2 x 0 2 2 2 3 3 x 1 4x (1 2x) 1 6x (1 2x) 1 4x (1 2x) lim lim lim x x x 1 4x (1 2x) 1 6x (1 2x) x lim lim x 1 4x (1 2x) x 1 6x (1 2x) 1 6x (1 2x) 4x (3 2x) lim x 1 6x (1 2x) 1 6x (1 2x) → → → → → → + − + + − + + − + = − = + + + + − + − − = + + + + + + + + + − + − + + + + + + 1 12 7 2 3 2 = − + = ………………….Hết………………… Nguồn : Hocmai.vn . Bài 1: Giới hạn dạng 0/0 - Khóa LTðH ñảm bảo – Thầy Phan huy Khải Hocmai.vn – Ngôi trường chung của học trò Việt 1 BTVN BÀI GIỚI HẠN DẠNG 0/0 Tính các giới hạn sau ñây: ( ) ( ) ( ) (. x 16 4 1 1 1 1 7 lim lim 6 8 24 x 9 3 x 16 4 → → → + + = + = + = + + + + Bài 1: Giới hạn dạng 0/0 - Khóa LTðH ñảm bảo – Thầy Phan huy Khải Page 2 of 3 ( ) ( ) ( ) ( ) ( ) ( ) (. 1 Còng nh− vËy ta cã : I lim 2 I I I I I 8 x → → = = + + + − = = ⇒ = + + + = Bài 1: Giới hạn dạng 0/0 - Khóa LTðH ñảm bảo – Thầy Phan huy Khải Page 3 of 3 ( ) ( ) ( ) ( ) ( ) ( ) (