Consider the following example.

- Observe that in Example 10.6.1, if we allow
to
approach 0
, we obtain a new function, say
That is,
let
- We can also write
- In the strict mathematical sense
does not exist. Hence,
mathematically speaking,
does not represent a
function.
- However, note that
- Also, observe that
Now, if we take the
limit of both sides, as
approaches zero (apply L'Hospital's
rule), we get

A K Lal 2007-09-12