f Cx )
Limits
i
-
Pca
q
)
at
~
L
L - - - ,
,h
I
-
a
f C x ) =
L I I K
p p →
" t RH
If the function is continuous
←
at a
tea f Gc ) =
fca ) =L
0ne-sidedlim
RH Limit LH Limit
¥ at
fcx ) =L tea - f Gc ) =L
x > a xLa
Relationship between limit and one - sided limit
×h→a+fCx ) =L
,¥a+ fad ¥a Stx )
}¥afCx
F
) =L
.
AND tea -
Sec ) =L THEN tea FCK ) DNE
#c→:
5- Cx )
Limit at
-
infinity
- -
- . -
- - -
-
in - - - -
- -
⇐ ±
f Cx ) =L
as
X
f- GD
' ⇒ → A
Infinite Limit ^ i
#
I
tea fcx ) = IN
I
I 2x
a
,
I
I
Vertical Asymptote
, Limit Laws
-
If TEA fed & xthagcx) both exist THEN
¥24 ] 2¥
tea I
I=qfEafc⇒
①
=
a
" =
4
e.g .
constant
# gcx ) ¥+242 txhze
"
② tea ffcsdtgcx ) ] = she,
a
fad ±
a
tea [ site ] =
e.g .
'
= 4 x e
schfaffcsd
god ] ¥afCx) # agcx ) ¥2 [24×2]=1%2 If
'
"
③ .
= x
e.g .
x zx
=
4×4=16
④
¥aKd=÷÷F ⇒
e
.
.÷s÷=÷÷÷s=÷=¥ -
Xo
"
)
"
] I Ea ¥32 )
"
⑤ Ihsa I Stx = HH
e.g
.
¥2 x
"
=
"
)
"
( ¥52 ( )
¥2
"
[22+2×+3] = x 2+2×+3
Isaiah
"
⑥ Fsa xD
#
"
[ "I
-
=
-
-
East
Limits
i
-
Pca
q
)
at
~
L
L - - - ,
,h
I
-
a
f C x ) =
L I I K
p p →
" t RH
If the function is continuous
←
at a
tea f Gc ) =
fca ) =L
0ne-sidedlim
RH Limit LH Limit
¥ at
fcx ) =L tea - f Gc ) =L
x > a xLa
Relationship between limit and one - sided limit
×h→a+fCx ) =L
,¥a+ fad ¥a Stx )
}¥afCx
F
) =L
.
AND tea -
Sec ) =L THEN tea FCK ) DNE
#c→:
5- Cx )
Limit at
-
infinity
- -
- . -
- - -
-
in - - - -
- -
⇐ ±
f Cx ) =L
as
X
f- GD
' ⇒ → A
Infinite Limit ^ i
#
I
tea fcx ) = IN
I
I 2x
a
,
I
I
Vertical Asymptote
, Limit Laws
-
If TEA fed & xthagcx) both exist THEN
¥24 ] 2¥
tea I
I=qfEafc⇒
①
=
a
" =
4
e.g .
constant
# gcx ) ¥+242 txhze
"
② tea ffcsdtgcx ) ] = she,
a
fad ±
a
tea [ site ] =
e.g .
'
= 4 x e
schfaffcsd
god ] ¥afCx) # agcx ) ¥2 [24×2]=1%2 If
'
"
③ .
= x
e.g .
x zx
=
4×4=16
④
¥aKd=÷÷F ⇒
e
.
.÷s÷=÷÷÷s=÷=¥ -
Xo
"
)
"
] I Ea ¥32 )
"
⑤ Ihsa I Stx = HH
e.g
.
¥2 x
"
=
"
)
"
( ¥52 ( )
¥2
"
[22+2×+3] = x 2+2×+3
Isaiah
"
⑥ Fsa xD
#
"
[ "I
-
=
-
-
East
