If $\lim_{x \to \infty} [\frac{x^2 + x + 1}{x + 1} - ax - b] = 3$, then $a - b = $

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

Let $k \in \mathbb{R}$. If $\lim _{x \rightarrow 0^{+}}(\sin (\sin k x)+\cos x+x)^{\frac{2}{x}}= e ^6$,then the value of $k$ is

If $n > 0$ and $\lim _{x \rightarrow 0} \frac{((a-n) n x-\tan x) \sin n x}{x^2}=0$,then the minimum value of $a$ is

Let $a$ be an integer such that $\lim \limits_{x \rightarrow 7} \frac{18-[1-x]}{[x]-3a}$ exists,where $[t]$ denotes the greatest integer function $\leq t$. Then $a$ is equal to:

If $\mathop {\lim }\limits_{x \to \infty } \left\{ {\ln \left( {{x^2} + 5x} \right) - 2\ln \left( {cx + 1} \right)} \right\} = -2$,then: