(the greek letter epsilon) (the greek letter delta) two positive small number
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(the Greek letter epsilon)
(the Greek letter delta)Two positive small number
2
4
2 424
4
2
5.12 x
2
4
2 424
4
2
22 x
2
4
2 424
4
2
5.03 x
2
4
2 424
4
2
ax
a
2
4
2 424
4
2
5.12 y
2
4
2 424
4
2
5.12)( xf
L
4
2 424
4
2
Lxf )(
Definition:
)(lim xf
ax
there is a positive number
for every positive number M
such that
)( then 0 if xfax
means that
x
y
y=1/x2
-6 -4 -2 0 2 4 60
1
2
3
4
5
6Example:
20
1lim
xx
Definition:
)(lim xf
ax
there is a positive number
for every positive number M
such that
)( then 0 if xfax
means that
x
y
y=1/x2
-6 -4 -2 0 2 4 60
1
2
3
4
5
6
Example:
20
1lim
xx
M
Definition:
)(lim xf
ax
there is a positive number
for every positive number M
such that
)( then 0 if xfax
means that
x
y
y=1/x2
-6 -4 -2 0 2 4 60
1
2
3
4
5
6
Example:
20
1lim
xx
000,10 ,100 ,4M
Mpositiveany
L Lxf )(
y=f(x)
a
ax
Definition:Lxf
ax
)(lim
there is a positive number
for every positive number
such that
Lxfax )( then 0 if
means that
Definition:Lxf
ax
)(lim there is a positive number
for every positive number
such that
Lxfax )( then 0 if
means that
Example:
31)2(lim 2
4
x
x
1)2()( 2 xxf
3)(lim4
xfx
1)2()( 2 xxf
3)(lim4
xfx
3.7321 4.23612361.0
2361.02679.0
113)( xf
2361.04 x
13)( then 2361.04 if xfx
f(x) is in here
when x is in here
13)( then 2361.04 if xfx
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
H
H
R
R
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
H
H
R
R
MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag