10個關於數字(e=2.7162....)的有趣事實(IN ENGLISH)

i^2 = -1 and pi = 3.14159 applies to all the following:

1)
e^x = 1 + x/1! + x^2/2! + x^3/3! +...

2)
e = 1 + 1/1! + 1/2! + 1/3!+ ...

when x = 1 for (1)

3)
e^(ix) = cosx + i sinx

when x = ix for (1)

4)
e^(i*pi) + 1 = 0

Connections to the symbols: e, pi, i, 1 and 0.

5)
e is one of the most important number to differentiation and integration.

6)
d(e^x)/dx = e^x

Derivative of this function is equal to itself

7)
d(lnx)/dx = 1/x where ln is the base e log (named natural log)

8)
2 = [e^1/e^(1/2)][e^(1/3)/e^(1/4)][e^(1/5)/e^(1/6)]....

9)
e = lim [(1 + 1/n)^n] when n tends to infinity

10)
e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427...
correct to 100 sigificant figures