The limit of a function
         Infinite limits
         The limit of a function examples
         Vertical, horizontal and slant (or oblique) asymptotes
Infinite limits
We write
if  f (x) can be made arbitrarily large by choosing x sufficiently close but not equal to a.
We write
if  f (x) can be made arbitrarily large negative by choosing x sufficiently close but not equal to a.
The limit of a function examples
Example:  Evaluate the following limits;
Solution:  a)  As x tends to minus infinity f (x)
gets closer and closer to 0. 
As x tends to plus infinity f (x) gets closer and
closer to 0. Therefore,
b)  As x tends to 0 from the left  f (x) gets larger in 
negative sense.
As x tends to 0 from the right  f(x) gets larger in positive sense. Therefore,
Vertical, horizontal and slant (or oblique) asymptotes
If a point (x, y) moves along a curve  f (x) and then at least one of its coordinates tends to infinity, while the distance between the point and a line tends to zero then, the line is called the asymptote of the curve.
Vertical asymptote
If there exists a number a such that
then the line  x = a  is the vertical asymptote.
Horizontal asymptote
If there exists a number c such that
then the line  y = c  is the horizontal asymptote.
Slant or oblique asymptote
If there exist limits
then, a line  y = mx + is the slant asymptote of the function  f (x).
Example:  Find the vertical and the horizontal
asymptote of the function
Solution:  Since,
then  x = 1  is the vertical asymptote.
Since,  
then  y = 2  is the horizontal asymptote.
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