$$ f(x) = \lim_{n\rightarrow \infty} \frac{nx}{1+n\sin(x)} = \lim_{n\rightarrow \infty}\frac{x/\sin(x)}{\frac{1}{n\sin(x)}+1} = \frac{x}{\sin(x)} \quad (x \neq 0) $$

and $$ f(0) =\lim_{n\rightarrow \infty} \frac{n(0)}{1+n\sin(0)} = 0 $$

but 
$$ \lim_{x\rightarrow 0+} f(x)=1$$

so $f$ is not continuous at $0$. The $f_n$ are all continuous at $0$ and if the sequence converged uniformly to $f$ then $f$ would be continuous at $0$. Since $f$ is not continuous at $0$ we can conclude that the sequence does not converge uniformly. 

How to prove that $f_n(x)=\frac{nx}{1+n\sin(x)}$ does not converge uniformly on $[0, \pi/2]$?
I have a new pond with a pump but the cable on the pump is far too short. I have some similar cable which will do the job to extend the length. My only concern is the junction outside. I need to make it dry and safe. What recommendations do people have? Can you buy a junction box that is suitable for outside use? If this helps I live in the UK.  
