What is the value of $\lim {\rm sup}_{n \to \infty} (x/n)$ Just a small question is the $\limsup_{n \to \infty} (x/n) = \infty$ .
Just getting confused since two variables are involved 
I am solving the following problem from Kenneth Ross 

For $x \in [0,\infty)$ , let $f_n= \frac xn$
a) Find $f(x) = \lim f_n(x)$
b) Determine whether $f_n \to f$ uniformly on $[0,1]$
c) Determine whether $f_n \to f$ uniformly on $[0,\infty)$

I found the following solution online 

So how is the solution arguing that $\limsup_{n \to \infty} (x/n) = \infty$ .

The variable $x$ can be factored out as it does not depend on the lim sup variable $n$. Thus,
$$
\limsup_{n \to \infty} \frac{x}{n}
= x \limsup_{n \to \infty} \frac{1}{n}
= x \cdot 0 = 0 \quad \forall \, x \,.
$$
