If lim(√(x^2-x+1) -ax) = b,then the ordered pair (a, b) is :

Question

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

lim(√(x²-x+1) -ax) = b

(1) (1,\(\frac{1}{2}\))

(2) (1,\(-\frac{1}{2}\))

(3) (-1,\(\frac{1}{2}\))

(4) (-1,\(-\frac{1}{2}\))

Answer 1

Option : (2) (1,\(-\frac{1}{2}\))

lim(√(x²-x+1) - ax) = b (∞-∞)

⇒ a > 0

Now,

Now,