Dirichlet Conditions/Examples/Sine of Reciprocal of x - 1

Example of Dirichlet Conditions
The function:
 * $\map f x = \map \sin {\dfrac 1 {x - 1} }$

does not satisfy the Dirichlet conditions on the real interval $\openint 0 {2 \pi}$.

Proof
Recall the Dirichlet conditions:

Around the point $x = 1$, $\map f x$ has an infinite number of local maxima and local minima.

Hence it does not satisfy Dirichlet condition $(\text D 2)$.