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 

 


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