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.