Notation of exponential function? What is the difference between this notation of the exponential function  
$$(1+\frac{1}{n})^n \rightarrow e  \\ \mathbf{as} \\ n \rightarrow \infty$$   
and this notation:  
$$\lim_{n\rightarrow \infty} (1+\frac{x}{n})^n$$

Why is there a variable $x$ in the second equation, and a $1$ in the first equation? That would make these limits not the same, yet wikipedia presents both as the exponential function. 

Indeed the limits are not the same. The second one is $e^x$. Only if you choose $x=1$, you get the first limit. The second one is more general.
