Symbolab Limits Cheat Sheet - Step by Step calculator
Symbolab Limits Cheat Sheet
Limit Properties:
If the limit of (), and () exists, then the following apply:
? lim =
?
lim (())
=
(lim
())
? lim[() ? ()] = lim () ? lim ()
? lim[ ()] = lim[()]
? lim[() ()] = lim () lim ()
?
lim
[()]
=
lim ()
,
where
lim () 0
()
lim ()
Limit to Infinity Properties:
For lim () = , lim () = , the following applies:
? lim[() ? ()] =
? lim[() ()] = , > 0
? lim[() ()] = -, < 0
?
lim
() ()
=
0
? lim = , 0 <
? lim = , is even, > 0
-
? lim = -, is odd, > 0
-
?
lim
=
0
Indeterminate Forms:
? 00
? 0
? 1
?
?
0 0
? 0
? -
Common Limits:
?
lim (1 + ) =
?
lim (
) = -
+
1
? lim(1 + ) =
0
Limit Rules:
? Limit of a Constant: lim =
? Basic Limit: lim =
? Squeeze Theorem: Let , and be functions such that for all [, ]
(except possible at the limit point c), () () (). Also suppse that
lim () = lim () = , then for any , , lim () =
?
L'Hopital's Rule :
For
lim
() ()
,
if
lim
() ()
=
0 0
or
lim
() ()
=
??, then
lim
() ()
=
lim
() ()
? Divergence Criterion: If there exists two sequences, {}=1 and {}=1
with: ,
and
lim
=
lim
=
,
lim
()
lim
(),
then lim () does not exist
? Limit Chain Rule: If lim () = , and lim () = , and () is continuous at
= , Then: lim (()) =
................
................
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