\mathop {\lim }\limits_{t \to 1 - } \frac{{t^x - 1}}
{{\ln t}} = \frac{0}
{0}\mathop = \limits^{L'H} \mathop {\lim }\limits_{t \to 1 - } \frac{{xt^{x - 1} }}
{{\frac{1}
{t}}} = x = f\left( {x,1} \right),\forall x \in \left[ {1,2} \right]