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

Example of Dirichlet Conditions
The function:
 * $f \left({x}\right) = \sin \left({\dfrac 1 {x - 1} }\right)$

does not satisfy the Dirichlet conditions on the real interval $\left({0 \,.\,.\, 2 \pi}\right)$.

Proof
Recall the Dirichlet conditions:

Around the point $x = 1$, $f \left({x}\right)$ has an infinite number of local maxima and local minima.

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