Number e
Calculating the number e = 2,7182… gives the limit
Explanation
The first derivative of the natural logarithm is
such that f ′(1) = 1. We use the definition of the derivative and write
Substitution of the logarithm gives
You can write this as the logarithm of a power
and since f ′(1) = 1 we get
The limit of a logarithm is the logarithm of a limit
such that
Therein, successive small values of x give
0,1 = 2,5937…
0,01 = 2,7048…
0,001 = 2,7169…
0,0001 = 2,7181…
0,00001 = 2,7182…
Note that for x = 0, the function is not defined.