Jacob Bernoulli introduced to address continuous compounding of interest, and defined as the following1.

The limit definition of is the following:

Using Limit Definition of to Solve Similar Limits

We can use the definition of to tackle similar limits: 2

We can prove the above relation by using change of variables: let , then

Footnotes

  1. e (mathematical constant) - Wikipedia

  2. Why can’t the 1/(3x) be replaced with 0? Reddit calculus limit r/calculus - YouTube