Infinite limits
Définition :
Infinite limits when the variable goes towards a finite value
Let
be an open interval of
an element of
and
an application from
to
We say that application
goes to
when
goes towards
if:
We write:
We define similarly an application which goes to
when
goes towards
if
One-sided limits
Let
and
be two real numbers,
and
an application from
to
We say that application
goes to
when
goes towards
from below if
We denote this by:
We say that application
goes to
when
goes to
from above if:
We denote this by:
Finite limits when the variable goes to infinity
We say that application
goes towards
when
goes to
if
We write:
We define similarly:
by:
Infinite limits when the variable goes to infinity
We say that application
goes to
when
goes to
if:
We write:
We define similarly
by:
by:
by:
Fondamental : Operations
Limits of a sum
The following table gives, when possible, the limit of the sum of applications
and
depending on the limits of
and
The symbol
(indetermined form) means there is no generic rule.
Limit of a product
The following table gives, when possible, the limit of the product of applications
and
depending on the limits of
and
Limit of a quotient
The following table gives, when possible, the limit of the quotient
depending on the limits of
and
We say that application
goes towards
if the limit is zero and the application has positive values.
We define similarly an application which goes towards
with negative values and the limit is then denoted by
