If $\lim _{x \rightarrow 3} \left( \frac{x^n - 3^n}{x - 3} \right) = 108$ and $n \in N$,then the value of $n$ is

The values of the constants $\alpha$ and $\beta$ such that $\lim_{x \to \infty} \left( \frac{x^2 + 1}{x + 1} - \alpha x - \beta \right) = 0$ are respectively:

If $\lim _{x}$ ${\rightarrow \infty} \frac{(\sqrt{2 x+1}+\sqrt{2 x-1})^8+(\sqrt{2 x+1}-\sqrt{2 x-1})^8(P x^4-16)}{(x+\sqrt{x^2-2})^8+(x-\sqrt{x^2-2})^8} = 1$,then $P=$

If $\lim_{x \to 1} \frac{x^3 + ax^2 + bx + c}{x^2 - 2x + 1} = 2026$, then the value of $a - c$ is...

If $\lim _{x \rightarrow \infty}\left(\frac{x^2+x+1}{x+1}-a x-b\right)=4$,then:

If $\alpha$ is the positive root of the equation $p(x) = x^{2} - x - 2 = 0$,then $\lim_{x \rightarrow \alpha^{+}} \frac{\sqrt{1 - \cos(p(x))}}{x + \alpha - 4}$ is equal to