Which of the following is correct. (Where[.] is G.I.F)

A) $x\to 0^{+}\Rightarrow x>0\Rightarrow e^x>1\left[e^x\right]=1$  $R.H.L=1\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}x<0^{-}\Rightarrow x<0e^x<1\left[e^x\right]=0$ L.H.L= indeterminate 

B) $x\to \frac{{\pi }^{+}}{2}\Rightarrow \cot x<\cot \frac{\pi }{2}\Rightarrow \left[\cot x\right]=-1$ $\therefore R.H.L=\pi L.H.L=\frac{\pi }{2}$

C) $\underset{x\to 0}{\lim }\frac{x}{x}=1$

D) Limit does not exist