Does e = limit as x tends to negative infinity hold true? Does $$e=\displaystyle\lim_{x \to -\infty}\left(1+\frac{1}{x}\right)^x\qquad\quad?$$
...or, in other words, rewrite the expression as 
$$
\lim_{y \to \infty} \frac{1}{\bigg(1-\frac{1}{y}\bigg)^y}
$$
if base tends to 1 after taking its separate limit and power tends to infinity
then use below formula this type of questions ...

       lim         (base-1)(power)
      x-&gt;infinity
    e