Part 3/7:
In 1727, the mathematician Leonhard Euler introduced the constant ( e ) to simplify calculations involving derivatives of exponential functions. Euler proposed seeking a number ( e ), such that the derivative at zero, ( f'(0) ), equals one. This effectively simplifies the process, allowing for a more straightforward calculation of derivatives.
The Derivative of ( e )
When we establish the number ( e ), we aim for the following limit to hold true:
[
\lim_{h \to 0} \frac{e^h - 1}{h} = 1
]