If the function f is defined as follows:

for x rational

for x irrational

How would you show that f is differentiable at ?

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- March 21st 2010, 03:58 PMCrazyCat87Differentiability of functions
If the function f is defined as follows:

for x rational

for x irrational

How would you show that f is differentiable at ? - March 21st 2010, 04:10 PMchiph588@

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 .