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

The values of $a$ and $b$ such that $\mathop {\lim }\limits_{x \to 0} \frac{{x(1 + a\cos x) - b\sin x}}{{{x^3}}} = 1$ are:

If $\mathop {\lim }\limits_{x \to 0} \frac{{\ln \left( {1 + x} \right) - ax}}{{{x^2}}} = l$,then the value of $(a + l)$ is equal to (where $l$ is a finite number).

If $\lim_{x \to 1} \frac{\sin(3x^2 - 4x + 1) - x^2 + 1}{2x^3 - 7x^2 + ax + b} = -2$, then the quadratic equation having roots $a$ and $b$ is

If $\mathop {Lim}\limits_{x \to 0} (x^{-3} \sin 3x + ax^{-2} + b)$ exists and is equal to zero,then:

If $\lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^4}\right)$ is finite,then the values of $a, b$ are respectively :