$\lim _{x \rightarrow 0} \left( \frac{3^{x}-1}{x} \right)$ is equal to

$\lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{1}{\left(x-\frac{\pi}{2}\right)^2} \int_{x^3}^{\left(\frac{\pi}{2}\right)^3} \cos \left(t^{1/3}\right) d t\right)$ is equal to

$\mathop {\lim }\limits_{x \to \pi /2} \frac{2x - \pi}{\cos x} = $

$\lim _{x \rightarrow 0} \left( \frac{x \cdot 10^x - x}{1 - \cos x} \right)$ is equal to

Let $x_0$ be the real number such that $e^{x_0}+x_0=0$. For a given real number $\alpha$,define $g(x)=\frac{3 x e^x+3 x-\alpha e^x-\alpha x}{3\left(e^x+1\right)}$ for all real numbers $x$. Then which one of the following statements is True?

The value of $\mathop {\lim }\limits_{x \to 0} \frac{2}{x}\log (1 + x)$ is equal to