 |
Limit
Limit[
expr
,
x
->
] finds the limiting value of expr when x approaches  .
Example: Limit[Sin[x]/x, x->0] .
Limit[
expr
,
x
->
,
Direction
->
1] computes the limit as  approaches  from smaller values. Limit[
expr
,
x
->
,
Direction
->
-1] computes the limit as  approaches  from larger values.
Limit returns Interval objects to represent ranges of possible values, for example at essential singularities.
Limit returns unevaluated when it encounters functions about which it has no specific information. Limit therefore makes no explicit assumptions about symbolic functions.
See the Mathematica book: Section 1.5.10, Section 3.6.8.
See also: Series, Residue.
Related package: NumericalMath`NLimit`.
Further Examples
This gives the limit of a symbolic expression.
In[1]:= 
Out[1]= 
This gives the limit of the tangent function at  approaching from the right.
In[2]:= 
Out[2]= 
Here is the limit approaching from the left.
In[3]:= 
Out[3]= 
Here is a symbolic polynomial in x.
In[4]:= 
Out[4]= 
This gives a symbolic limit assuming the function fn to be an analytic function.
In[5]:= 
Out[5]= 
If you do not use Analytic
->
True, L'Hopital's rule will not be used and the limit cannot be evaluated.
In[6]:= 
Out[6]= 
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | | | |
| |
|
