Approximate the limit of the function $f(x) = \left( 1+x \right)^{1/x}$ as $x$ approaches $0$ numerically and graphically.

1. Evaluate the function $f$ at the following values of $x$ near zero. Enter at least four decimal places.

   $x$	$f(x) = \left( 1+x \right)^{1/x}$
   $-0.01$
   $-0.001$
   $-0.0001$
   $0$	undefined
   $0.0001$
   $0.001$
   $0.01$

2. Find an approximate value for the limit. The answer should be a familiar transcendental number.
   $\displaystyle{\lim_{x \to 0} \left( 1+x \right)^{1/x} \approx}$ . Your answer should be accurate to four decimal places.