MCQ
The value of the constant $\alpha $ and $\beta $ such that $\mathop {\lim }\limits_{x \to \infty } \left( {\frac{{{x^2} + 1}}{{x + 1}} - \alpha x - \beta } \right) = 0$ are respectively
- A$(1, 1)$
- B$(-1, 1)$
- ✓$(1, -1)$
- D$(0, 1)$
==> $\mathop {\lim }\limits_{x \to \infty } \frac{{{x^2}(1 - \alpha ) - x(\alpha + \beta ) + 1 - b}}{{x + 1}} = 0$
Since the limit of the given expression is zero, therefore degree of the polynomial in numerator must be less than denominator.
$\therefore$ $1 - \alpha = 0$ and $\alpha + \beta = 0$
==> $\alpha = 1$ and $\beta = - 1$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.