# What is the value of exponential e?We know this value is varying between 2 and 3. But what is its actual value?

## What is the value of exponential e?We know this value is varying between 2 and 3. But what is its actual value?

In mathematics, the constant e has a number of important properties. The brief answer to your question is that it has a value of     e=2.7182818284  (to ten decimal places)It is defined as the function f(x)=e^x whose derivative at the point x=0 is exactly 1. That is, the slope of the tangent line at x=0 is 1. For other numbers, the slope of the tangent line is not exactly 1. Another definition of e is that it is the number given by the limit as n approaches infinity of     (1+ 1/n)^nIts usefulness lies in its properties. For one, the derivative of     f(x)=e^xis     f'(x)=e^xand for other exponential functions, the derivative of something like     f(x)=e^axis     f'(x)=a*e^axAnother useful property is its relationship to complex numbers. We define Euler’s formula ase^ix = cos x + i sin xgiving rise to trigonometric representations on a graph in the complex plane.
What is the value of exponential e?We know this value is varying between 2 and 3. But what is its actual value?
What is the value of exponential e?We know this value is varying between 2 and 3. But what is its actual value?