If $\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} - x + 1} - ax} \right) = b$, then the ordered pair (a, b) is :

Question

$\left( {1,{1 \over 2}} \right)$

$\left( {1, - {1 \over 2}} \right)$

$\left( { - 1,{1 \over 2}} \right)$

$\left( { - 1, - {1 \over 2}} \right)$

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