a) \(\mathop {\lim }\limits_{t \to {1^ + }} \left( {x - 2} \right) = - 1 < 0\)
\(\mathop {\lim }\limits_{t \to {1^ + }} \left( {x - 1} \right) > 0\;\)
\( \Rightarrow \mathop {\lim }\limits_{t \to {1^ + }} \frac{{x - 2}}{{x - 1}} = - \infty \;\)
b) \(\mathop {\lim }\limits_{t \to {4^ - }} \left( {{x^2} - x + 1} \right) = 13 > 0\)
\(\mathop {\lim }\limits_{t \to {4^ - }} \left( {4 - x} \right) > 0\)
\( \Rightarrow \mathop {\lim }\limits_{t \to {4^ - }} \frac{{{x^2} - x + 1}}{{4 - x}} = + \infty \;\)
