Infinite Limits

Vertical Asymptotes

Consider the function 

        f(x) = x/(x - 1)  

From the graph we see that there is a vertical asymptote at x = 1.  We say

       
and

       

Formal Definition

 

Definition   We say             if for any choice of N there exists a d such that whenever            |x - c|  <  d  then            |f(x)|  >  N

Example

Prove that

       

Solution

Let N be given then choose d such that

        1/d > N

We have that if

        x - 2  <  d

then

         1               1
                   >            >   N
       x - 2            d      

Hence the limit is infinity.

Other Sites on Limits

Karl's Calculus

Visual Calculus

Ohio State Calculus

Weisstein's World of Mathematics

Dr. Sloanes Calculus 

Back to Math 105 Home Page

e-mail Questions and Suggestions