Limit Definition of e

Question

Evaluate $$\lim_{x 	o \infty} \left(1 + \frac{1}{x}ight)^{x}$$.

Accepted Answer

$$e$$

Answer

$$0$$

Answer

$$1$$

Answer

A misapplication of the limit definition for the exponential function may lead one to mistakenly conclude that the limit is $$1$$, but it converges to the constant $$e$$.