If the function f is defined as follows:
for x rational
for x irrational
How would you show that f is differentiable at ?
We need to show this limit exists when .
For this we need to compare and .
For , , so our will only consider the sequence containing all points of the form .
Thus .
Clearly our will only consider the sequence containing all points of the form .
Thus .
Since , exists and equals .
Therefore .