Maths (commerce) Solve the Following Question.(4 Marks)

$\lim _{x \rightarrow 0}\left[\frac{\left(2^x-1\right)^2}{\left(3^x-1\right) \cdot \log (1+x)}\right]$

$\lim _{x \rightarrow 0}\left[\frac{\log (2+x)-\log (2-x)}{x}\right]$

$\lim _{x \rightarrow 2}\left[\frac{x^3-8}{\sqrt{x+2}-\sqrt{3 x-2}}\right]$

$\lim _{x \rightarrow 0}\left[\frac{\sqrt{1+x^2}-\sqrt{1+x}}{\sqrt{1+x^3}-\sqrt{1+x}}\right]$

$\lim _{x \rightarrow a}\left[\frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}\right]$

$\lim _{x \rightarrow 2}\left[\frac{\sqrt{2+x}-\sqrt{6-x}}{\sqrt{x}-\sqrt{2}}\right]$