If $\mathop {\lim }\limits_{x \to \infty } \left\{ {\sqrt {{x^2} - x + 1} - ax - b} \right\} = 0$, then

JEE MATHEMATICS MCQ: LIMITS

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\lim\limits_{x \to \infty } \left\{ {\sqrt {{x^2} - x + 1} - ax - b} \right\} = 0

, then

View answer and explanation

Correct option: B

a = 1,\;b = - \frac{1}{2}

Option B (

a = 1, b = -\frac{1}{2}

) is correct because after rationalizing and comparing coefficients, these are the values that make the limit equal to 0.

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