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GIÔÙI HAÏN HAØM SOÁ 1.[r]
(1)2 GIỚI HẠN HAØM SỐ 1. Dùng định nghĩa, CMR:
a) lim(2x 3) 7x 2 b) x
x
lim
2(x 1)
c)
2 x
x 3x
lim
x
2. Tìm giới hạn sau
a)
3
x
lim(x 5x 10x)
b)
2 x
x 5x
lim
x
c) lim x 1x 3 d)
2 x
2x 3x
lim
x 4x
e) x
1
lim
1 x 2x
f)
2 x
x lim
x 3x
g) x
1 x x lim
x
h) x sin x lim
x
i) lim
cos
x x j)
tan sin2x lim
cos x
x x
k)x tgx lim
x
Dạng vô định 0 3. Tìm giới hạn sau: a)
2 x
x lim
x 3x
b)
2
x
x lim
x 3x
c)
2 x
x 5x lim
x 25
d)
2 x
x 2x lim
2x 6x
e)
3 x
x 3x lim
x 4x
f)
3
2 x
x x x
lim
x 3x
g)
2
2
lim
8
x
x x
x
h)
4
2
72 lim
2 x
x x
x x
i)
5
1 lim
1
x x x
j)
3
4
x
x 5x 3x lim
x 8x
k)
4
3
x
2x 8x 7x 4x
lim
3x 14x 20x
l)
3
3
x
x 3x 9x
lim
x x
m)
2
lim
1
x x x
n)
1
lim
1
x x x
o)
5
2 x
x 5x 4x lim
(1 x)
p)
3
h
(x h) x lim
h
q)
2
3
x a
x (a 1)x a lim
x a
r)
4
x a
x a
lim x a
s)
3
h
2(x h) 2x
lim
h
t) x 2
x x
lim
x 5x 3(x 3x 2)
u)
1992 1990 x
x x
lim
x x
k)
n
2 x
x nx n
lim
(x 1)
Tìm giới hạn sau:
A = x
18 x x lim 3
2
x
B =
2 x
x x 30
lim
2x 9x
C = x
x lim
x 2x x
D =
2
3
1 x
2
4x
lim
4x 2x
(2)E = 2 x
x 4x
lim
x 2x
F =
2 x
2
2x 5x
lim
4x
G =
2 x
2x 3x
lim
x 4x
H =
4 x
x 16
lim
x 2x
I = x
x
lim
x x
J = x 4x 27 x lim 2
3
x
K =
3
2 x
x 6x 12x
lim
x 4x
L =
3
2 x
x x x
lim
x 5x
M =
3 x
8x 64
lim
x 5x
N =
3
3 x
x 2x 6x
lim
8 x
O =
3
2 x
x x 5x
lim
x 3x
P =
3
2 x
x 4x 6x
lim
x x
Q = x
x 3x
lim
x 2x
R =
5 x
x
lim
x
Tìm giới hạn sau:
a)
2 x
x x x
lim
x
b) x x lim
49 x
c) x 2
2 x
lim
x 3x
d) EMBED
Equation.DSMT4x 2
4x lim
x
e) EMBED Equation.DSMT4 x
2x lim
x 4x
f) EMBED Equation.DSMT4
x
x 2x lim
x
g) EMBED Equation.DSMT4
2
2
lim
3 x
x
x x
h) EMBED Equation.DSMT4
3
2 lim
8 x
x x
x
i)
2 x
3x 4x x
lim
x 3x
j) EMBED Equation.DSMT4 x
3 x lim
1 x
k) EMBED
Equation.DSMT4 x
3 x lim
2x x
l) EMBED Equation.DSMT4x
x x
lim
4x
EMBED Equation.DSMT4
2
2 ) lim
2 x
x x x
m
x x
n) EMBED Equation.DSMT4
4
3
x
x lim
x x
o) EMBED Equation.DSMT4
3
1 lim
2 x
x x x
p) EMBED Equation.DSMT4
3
1 lim
2
x
x
x x
q) EMBED Equation.DSMT4
2 x
2x 12 x lim
x 2x
r) EMBED Equation.DSMT4
3 x
x lim
x
s)
EMBED Equation.DSMT4
1 lim
1 x
x x
t) EMBED Equation.DSMT4 x
x lim
x
(3)v) EMBED Equation.DSMT4 x
x lim
x
w) EMBED Equation.DSMT4
3 x
x lim
4x
x) EMBED Equation.DSMT4
3
2 x
x x lim
(x 1)
Tính giới hạn sau:
a x
x x
lim
x
b x0 x9x167
lim
x
c
3 x
x x lim
x
d
3 x
x x lim
x
e
3
3
lim
1
x
x x
x
f
3 x
8x 11 x lim
x 3x
Dạng vô định
7.Tìm giới hạn sau: a) x
2x lim
x
b)
2 x
x lim
1 3x 5x
c)x
x x lim
x x
d)
2 x
3x(2x 1) lim
(5x 1)(x 2x)
e)
3
3
3 2
lim
2
x
x x
x x
f)
3
4
3
lim
4
x
x x
x x
g)
3
2
2
lim
3
x
x x
x x
h)
4
3
3
lim
2 x
x x
x x
i)
2
4 x
(x 1) (7x 2) lim
(2x 1)
j)
2
2
x
(2x 3) (4x 7) lim
(3x 4) (5x 1)
k)
2 x
4x
lim
3x
l)
2 3 2
lim
3 x
x x x
x
m)
2 3 2
lim
3 x
x x x
x
n)
2 x
x x 3x lim
4x 1 x
o)
2 x
4x 2x x
lim
9x 3x 2x
p)
2 x
x 2x 4x
lim
4x x
q)x
x x lim
x
r)
3 2 lim
2 x
x x x
x
s)
3
3 2 2
3
2
( )
lim
3
x
x x x x x x
x x
t)x
(x x x 1)( x 1) lim
(x 2)(x 1)
Dạng vô định
8.Tính giới hạn sau: a) lim(2 )
3 x
x
x b)
3
lim (2 )
x x x c)
2
lim
x x x d)
2
xlim ( x x x)
e)
2
xlim ( x x x) f) lim( )
2 x x
x
x g) lim( )
2 x x
x
x h)
2
(4)i) xlim( x2 x 2) j)
2
xlim ( x 4x 3 x 3x 2) k)
2
lim ( )
x x x x
l)
2
xlim (2x 1 4x 4x 3) m)
2
xlim (3x 2 9x 12x 3)
n)lim( 2)
2
x x x
x
o) lim( 2)
2
x x x
x p)
2
lim ( 1)
x x x x q)
2
lim ( 3) x x x x
r)
2
lim ( 1)
x x x x s)
3
xlim ( x x x) t)
3
xlim ( x x x x)
v)
3
2
xlim ( x x 1)
w)
3
lim ( )
x x x x x
Giới hạn bên
9 Tìm giới hạn sau
a)
2
2
2 lim
3 x
x x
x
b)
3 lim
2 x
x
c) 1 lim
1 x
x x
d)
1 lim
1 x
x x
e)
2
x
x x lim
2x
f) x
2x lim
4x x
g)
3 lim
2
2
x
x x
x h)
3 lim
2
2
x
x x
x i)
3 lim
4 x
x x
j)
3 lim 2
2
2
x x
x x x
k)
3 lim 2
2
2
x x
x x
x l)
3 x
x 3x lim
x 5x
g)x
1 x lim x
x
h)
2 x
x x lim
x
i)x
1 cos2x lim
x
10 Tìm giới hạn bên phải, giới hạn bên trái hs f(x) xo xét xem hàm số có giới hạn xo khơng ?
2
o
x 3x (x 1) x
a) f(x)
x (x 1)
với x
2
o
4 x (x 2) b) f(x) x 2
1 2x (x 2) với x
3
1 x
x c) f (x) 1 x 1
3/ x
0 o
với x
11 Tìm A để hàm số sau có giới hạn xo:
a)
3
x 1 (x 1) f(x) x 1
Ax (x 1)
với x0 = b)
3
2
x 2x
A x
f (x) x 4x 3x
3x x
với x0 = 3
(5)12 Tính giới hạn sau: a) x
sin 5x lim
3x
b) x
1 cos2x lim
x
c)x
cosx cos7x lim
x
d) x
cosx cos3x lim
sin x
e)x tgx sin x lim
x
f)x
1
lim x
sin x sin3x
g)
sin sin lim
3sin x
x x
x
h)
1 sin cos2 lim
sin x
x x
x