Symbolab Limits Cheat Sheet - Step by Step calculator

[Pages:2]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 (()) =

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download