x 0.9 0.99 0.999 0.9999 1 ( )f x 2.8 2.98 2.998 2.9998 3
1 x 1 1.0001 1.001 1.01 1.1
( )f x 3 3.002 3.002 3.02 3.2 2
1 ( ) ( )f x 3 x 1
1lim ( ) 3x
f x
2 () ( )f x 3 x 1
1lim ( ) 3x
f x
( )f x 3 x ( )f x 3 x 1
1lim ( ) 3x
f x
1
2
3
1 2 3 x
y
01
( ) 2 1f x x
E-learning 25 -02-55
2
f x a ( x a ) lim ( ) lim ( )
x a x af x f x
lim ( )
x af x
a 1. lim
x ac c
c
2. limx a
x a
3. lim lim , lim , lim , lim
x a xx a x a lim
x
1lim ( )f x L 2lim ( )g x L 3.1 1 2lim ( ) ( ) lim ( ) lim ( )f
x g x f x g x L L 3.2 1 2lim ( ) ( ) lim ( ) lim ( )f x g x f x g x
L L 3.3 1 2lim ( ) ( ) lim ( ) lim ( )f x g x f x g x L L 3.4 1
2
( ) lim ( )lim
( ) lim ( )
Lf x f x
g x g x L 2 0L
3.5 1lim ( ) lim ( ) c f x c f x cL 3.6 1lim ( ) lim ( )n n nf x
f x L n L 3.7 lim ( ) lim ( )n n nf x f x L 4. p 4.1 1lim 0
px x
4.2 1lim 0px x
lim ( )x a
f x L
lim ( ) lim ( )x a x a
f x f x L
L
E-learning 25 -02-55
3
1 21
lim(3 2)x
x
2 2
1 11lim(3 2) 3lim lim 2x xx
x x
2
1 3 lim 2
xx
2 3 1 2 3 2 5 # 2 11 1 0( ) ...n nn nf x c x c x c x c lim (
)
x af x
11 1 0lim ( ) lim lim ... lim limn nn nx a x a x a x a x a
f x c x c x c x c
1
1 1 0 lim lim ...n n
n nx a x a
c x c x c a c
11 1 0 ...n nn nc a c a c a c ( )f a lim ( ) ( )
x af x f a
#
5. lim ( ) 0f x lim ( ) 0g x ( ) 0lim
( ) 0
f x
g x
6. lim ( )f x lim ( )g x ( )lim
( )
f x
g x
( ) 0lim
( ) 0
f x
g x
0
0
00
(1) (2)
mx m x ( )f x ( )g x (
)
E-learning 25 -02-55
4
3 3
lim ( )x
f x
2 5 , 3
( )13 , 3
x xf x
x x
( )f x x 3 2( ) 5f x x x 3 ( ) 13f x x
3lim ( )x
f x
3
lim ( )x
f x
2 2
3 3lim ( ) lim( 5) 3 5 4x x
f x x
3 3 3lim ( ) lim( 3) lim( 3) 3 13x x x
f x x x
16 4
3 3 lim ( ) lim ( ) 4x x
f x f x
3lim ( ) 4x
f x
# 4
3
2 5 1lim
3xx
x
3 3
2 5 1 2 5 1 2 5 1lim lim( ) ( )
3 3 2 5 1x xx x x
x x x
3
2( 3) lim
( 3)( 2 5 1)xx
x x
3
2 lim
( 2 5 1)x x
33
lim 2
lim( 2 5 1)x
xx
2 2
1 #
E-learning 25 -02-55
5
5 2
4lim
3 7xx
x
2
4
3 7
x
x
x 2 2x
1lim 0 ; 0px
px
22
2
1 44
lim lim 73 7 3
x x
x x xx
x
22
1 4lim( )
7
lim(3 )
x
x
x x
x
22
1 1lim 4lim
1
lim3 7 lim
x x
x x
x x
x
0 4(0) 0 03 7(0) 3
#
6
2 4lim
2xx
x
1 2
2 2
4(1 )
4 lim lim
2 2x x
xx xx x
2
2
4( ) 1
lim2x
xx
x
24
( ) 1 lim
2x
xx
x
24
( ) 1 lim
2x
xx
x
24
1 lim
21
x
x
x
24
lim 1
2lim ( 1 )
x
x
x
x
E-learning 25 -02-55
6
24
lim (1 )
2lim 1 lim
x
x x
x
x
1 11
#
f x a lim ( ) ( )x a
f x f a
f x a 1. ( )f a 2. lim ( )
x af x
3. lim ( ) ( )x a
f x f a
f f x a f ( , )a b f ( , )x a b f ( , ) f 1 2 , 1 ( )
-1 , 1
xf x
x
f 1x ( 1) 2f
1 1lim ( ) lim ( 1) 1x x
f x
1 1lim ( ) lim 2 2x x
f x
1 1lim ( ) lim ( )x x
f x f x
1lim ( )x
f x
f 1x
1 2011
1
2
x
y2 , 1
( )1 , 1
xf x
x
E-learning 25 -02-55
7
2 ( )f x x 0x ( )f x x , 0( )
, 0
x xf x
x x
(0) 0f
0 0lim ( ) lim 0x x
f x x
0 0lim ( ) lim( ) 0x x
f x x
0lim ( ) 0 (0)x
f x f
f 0x
3 2
, 1
( ) 3 , 1 2
, 2
ax b x
f x x x
bx a x
a b f x = 1 x = 2 f x = 1
1lim ( )x
f x
1 1lim ( ) lim ( )x x
f x f x
1 1lim ( ) lim (3 )x x
ax b x
3a b .........(1) f 2x
2lim ( )x
f x
2 2lim ( ) lim ( )x x
f x f x
2
2lim(3 ) lim( )x
x bx a
6 4b a 4 6a b .........(2) (1) (2) 3b 3a b f 1x 2x 3a b 3b a b
#
![H20youryou[2] · 2020. 9. 1. · 65 pdf pdf xml xsd jpgis pdf ( ) pdf ( ) txt pdf jmp2.0 pdf xml xsd jpgis pdf ( ) pdf pdf ( ) pdf ( ) txt pdf pdf jmp2.0 jmp2.0 pdf xml xsd](https://img.pdfslide.tips/doc/110x75/60af39aebf2201127e590ef7/h20youryou2-2020-9-1-65-pdf-pdf-xml-xsd-jpgis-pdf-pdf-txt-pdf-jmp20.jpg)
