Section 1 6-Limit
. Laws 08/29/2022
Math 224
suppose C is a constant
imf(x) L and
im g(x) =
=
, ,
1) lim
X > A
[f(x) Ig(x)) = L [m =
limf(x)
#
limy
2) lim Cf(x) = CL = Climf(x)
X > X3@
3) limf(x)g(x) limf(x)
<m
Limg(x)
= = ·
X A > X >a
> (x)
-
lim f(x)
4) = i =
/img(x) , provided limg(x) = O
lim g(x)
X >&
5)/im [f(x)] [mf(x)] where is
integer h
=
,
n a positive
6
/im =
1) limx = &
X >a
8) limx =
an
X >
=
9)
limax
"imf(x)
10)
limnf(x) where integer (If
limf(xs
=
,
is a positive .
h is even
,
we assume
X >
.)
positive
Examples :
1) Evaluate (2x2 4)
Lim 3x +
-
lim(2x"-3x + 4)
X)S
<
/im (2x) +
/im (-3X) + lim (4)
X >S
<2 .
lim(X4)-
X >S
3 .
Lim(x) + lim
X >S
(4)
< 2(25) -
3(5) + 4 = 39
lim(2x2 -
3x + 4) =
39
XS
X3 -
2x2 - 1
2) Evaluate lim S-3x
X3 -
2
x3 2x2 1 ( 2(3 2) 2) 1,
851 Th
- - - -
- - -
> =
lim S -
3X S -
3) 2)
-
Xy -
2
X3 2x2 1
in
- -
lim
=
-
S-3x
X3 2 -
X3 -
2X2 -
1
substitution Both lim (2x2-3X + 4) and lim be
Direct :
X >5 X3 2
-
S-3x can computed by
the features the limit
calculating at .
point
. Laws 08/29/2022
Math 224
suppose C is a constant
imf(x) L and
im g(x) =
=
, ,
1) lim
X > A
[f(x) Ig(x)) = L [m =
limf(x)
#
limy
2) lim Cf(x) = CL = Climf(x)
X > X3@
3) limf(x)g(x) limf(x)
<m
Limg(x)
= = ·
X A > X >a
> (x)
-
lim f(x)
4) = i =
/img(x) , provided limg(x) = O
lim g(x)
X >&
5)/im [f(x)] [mf(x)] where is
integer h
=
,
n a positive
6
/im =
1) limx = &
X >a
8) limx =
an
X >
=
9)
limax
"imf(x)
10)
limnf(x) where integer (If
limf(xs
=
,
is a positive .
h is even
,
we assume
X >
.)
positive
Examples :
1) Evaluate (2x2 4)
Lim 3x +
-
lim(2x"-3x + 4)
X)S
<
/im (2x) +
/im (-3X) + lim (4)
X >S
<2 .
lim(X4)-
X >S
3 .
Lim(x) + lim
X >S
(4)
< 2(25) -
3(5) + 4 = 39
lim(2x2 -
3x + 4) =
39
XS
X3 -
2x2 - 1
2) Evaluate lim S-3x
X3 -
2
x3 2x2 1 ( 2(3 2) 2) 1,
851 Th
- - - -
- - -
> =
lim S -
3X S -
3) 2)
-
Xy -
2
X3 2x2 1
in
- -
lim
=
-
S-3x
X3 2 -
X3 -
2X2 -
1
substitution Both lim (2x2-3X + 4) and lim be
Direct :
X >5 X3 2
-
S-3x can computed by
the features the limit
calculating at .
point
