AP EAMCET · Maths · Limits
If \(\lim _{x \rightarrow \infty}\left\{\frac{x^3+1}{x^2+1}-(\alpha x+\beta)\right\}\) exists and equal to 2 , then the ordered pair \((\alpha, \beta)\) of real numbers is
- A \((1,-1)\)
- B \((-2,1)\)
- C \((-1,1)\)
- D \((1,-2)\)
Answer & Solution
Correct Answer
(D) \((1,-2)\)
Step-by-step Solution
Detailed explanation
It is given that, \(\begin{aligned} & \lim _{x \rightarrow \infty}\left\{\frac{x^3+1}{x^2+1}-(\alpha x+\beta)\right\}=2 \\ & \Rightarrow \lim _{x \rightarrow \infty} \frac{x^3+1-\alpha x^3-\beta x^2-\alpha x-\beta}{x^2+1}=2 \end{aligned}\) For the existance of limit, coefficient…
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