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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