Fundamental Mathematics/Calculus/Limit

LimitEdit

 

Finite Limit We call   the limit of   as   approaches   if   becomes arbitrarily close to   whenever   is sufficiently close (and not equal) to   .

When this holds we write

 

or

 


Infinite Limit We call   the limit of   as   approaches infinity if   becomes arbitrarily close to   whenever   is sufficiently large.

When this holds we write

 

or

 

Similarly, we call   the limit of   as   approaches negative infinity if   becomes arbitrarily close to   whenever   is sufficiently negative.

When this holds we write

 

or