JEE Mains · Maths · STD 11 - 12. limits
If \(\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-x+1}-a x\right)=b\), then the ordered pair \((a, b)\) is:
- A \(\left(1, \frac{1}{2}\right)\)
- B \(\left(1,-\frac{1}{2}\right)\)
- C \(\left(-1, \frac{1}{2}\right)\)
- D \(\left(-1,-\frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(B) \(\left(1,-\frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-x+1}\right)-a x=b \quad(\infty-\infty)\) \(\Rightarrow a>0\) Now, \(\lim _{x \rightarrow \infty} \frac{\left(x^{2}-x+1-a^{2} x^{2}\right)}{\sqrt{x^{2}-x+1}+a x}=b\)…
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