 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.   Functions contents E 